-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathfft.html
1774 lines (1565 loc) · 160 KB
/
fft.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
<meta name="robots" content="noindex">
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>torch.fft — PyTorch 1.8.1 documentation</title>
<link rel="canonical" href="https://pytorch.org/docs/stable/fft.html"/>
<link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
<!-- <link rel="stylesheet" href="_static/pygments.css" type="text/css" /> -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" type="text/css" />
<link rel="stylesheet" href="_static/css/jit.css" type="text/css" />
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" type="text/css" />
<link rel="stylesheet" href="_static/katex-math.css" type="text/css" />
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="torch.futures" href="futures.html" />
<link rel="prev" title="Probability distributions - torch.distributions" href="distributions.html" />
<script src="_static/js/modernizr.min.js"></script>
<!-- Preload the theme fonts -->
<link rel="preload" href="_static/fonts/FreightSans/freight-sans-book.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/FreightSans/freight-sans-medium.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/IBMPlexMono/IBMPlexMono-Medium.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/FreightSans/freight-sans-bold.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/FreightSans/freight-sans-medium-italic.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/IBMPlexMono/IBMPlexMono-SemiBold.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<!-- Preload the katex fonts -->
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Math-Italic.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Main-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Main-Bold.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size1-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size4-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size2-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size3-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Caligraphic-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.15.2/css/all.css" integrity="sha384-vSIIfh2YWi9wW0r9iZe7RJPrKwp6bG+s9QZMoITbCckVJqGCCRhc+ccxNcdpHuYu" crossorigin="anonymous">
</head>
<div class="container-fluid header-holder tutorials-header" id="header-holder">
<div class="container">
<div class="header-container">
<a class="header-logo" href="https://pytorch.org/" aria-label="PyTorch"></a>
<div class="main-menu">
<ul>
<li>
<a href="https://pytorch.org/get-started">Get Started</a>
</li>
<li>
<a href="https://pytorch.org/ecosystem">Ecosystem</a>
</li>
<li>
<a href="https://pytorch.org/mobile">Mobile</a>
</li>
<li>
<a href="https://pytorch.org/blog/">Blog</a>
</li>
<li>
<a href="https://pytorch.org/tutorials">Tutorials</a>
</li>
<li class="active">
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="resource-option with-down-orange-arrow">
Docs
</a>
<div class="resources-dropdown-menu">
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/docs/stable/index.html">
<span class="dropdown-title">PyTorch</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/audio/stable/index.html">
<span class="dropdown-title">torchaudio</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/text/stable/index.html">
<span class="dropdown-title">torchtext</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/vision/stable/index.html">
<span class="dropdown-title">torchvision</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/elastic/">
<span class="dropdown-title">TorchElastic</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/serve/">
<span class="dropdown-title">TorchServe</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/xla">
<span class="dropdown-title">PyTorch on XLA Devices</span>
<p></p>
</a>
</div>
</li>
<li>
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="resource-option with-down-arrow">
Resources
</a>
<div class="resources-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/features">
<span class="dropdown-title">About</span>
<p>Learn about PyTorch’s features and capabilities</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/#community-module">
<span class="dropdown-title">Community</span>
<p>Join the PyTorch developer community to contribute, learn, and get your questions answered.</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/resources">
<span class="dropdown-title">Developer Resources</span>
<p>Find resources and get questions answered</p>
</a>
<a class="nav-dropdown-item" href="https://discuss.pytorch.org/" target="_blank">
<span class="dropdown-title">Forums</span>
<p>A place to discuss PyTorch code, issues, install, research</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/hub">
<span class="dropdown-title">Models (Beta)</span>
<p>Discover, publish, and reuse pre-trained models</p>
</a>
</div>
</div>
</li>
<li>
<a href="https://github.com/pytorch/pytorch">Github</a>
</li>
</ul>
</div>
<a class="main-menu-open-button" href="#" data-behavior="open-mobile-menu"></a>
</div>
</div>
</div>
<body class="pytorch-body">
<div class="table-of-contents-link-wrapper">
<span>Table of Contents</span>
<a href="#" class="toggle-table-of-contents" data-behavior="toggle-table-of-contents"></a>
</div>
<nav data-toggle="wy-nav-shift" class="pytorch-left-menu" id="pytorch-left-menu">
<div class="pytorch-side-scroll">
<div class="pytorch-menu pytorch-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
<div class="pytorch-left-menu-search">
<div class="version">
<a href='https://pytorch.org/docs/versions.html'>1.8.1 ▼</a>
</div>
<div role="search">
<form id="rtd-search-form" class="wy-form" action="search.html" method="get">
<input type="text" name="q" placeholder="Search Docs" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<p class="caption"><span class="caption-text">Notes</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="notes/amp_examples.html">Automatic Mixed Precision examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/autograd.html">Autograd mechanics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/broadcasting.html">Broadcasting semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/cpu_threading_torchscript_inference.html">CPU threading and TorchScript inference</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/cuda.html">CUDA semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/ddp.html">Distributed Data Parallel</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/extending.html">Extending PyTorch</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/faq.html">Frequently Asked Questions</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/large_scale_deployments.html">Features for large-scale deployments</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/modules.html">Modules</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/multiprocessing.html">Multiprocessing best practices</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/randomness.html">Reproducibility</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/serialization.html">Serialization semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/windows.html">Windows FAQ</a></li>
</ul>
<p class="caption"><span class="caption-text">Language Bindings</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="cpp_index.html">C++</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/javadoc/">Javadoc</a></li>
</ul>
<p class="caption"><span class="caption-text">Python API</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="torch.html">torch</a></li>
<li class="toctree-l1"><a class="reference internal" href="nn.html">torch.nn</a></li>
<li class="toctree-l1"><a class="reference internal" href="nn.functional.html">torch.nn.functional</a></li>
<li class="toctree-l1"><a class="reference internal" href="tensors.html">torch.Tensor</a></li>
<li class="toctree-l1"><a class="reference internal" href="tensor_attributes.html">Tensor Attributes</a></li>
<li class="toctree-l1"><a class="reference internal" href="tensor_view.html">Tensor Views</a></li>
<li class="toctree-l1"><a class="reference internal" href="autograd.html">torch.autograd</a></li>
<li class="toctree-l1"><a class="reference internal" href="cuda.html">torch.cuda</a></li>
<li class="toctree-l1"><a class="reference internal" href="amp.html">torch.cuda.amp</a></li>
<li class="toctree-l1"><a class="reference internal" href="backends.html">torch.backends</a></li>
<li class="toctree-l1"><a class="reference internal" href="distributed.html">torch.distributed</a></li>
<li class="toctree-l1"><a class="reference internal" href="distributions.html">torch.distributions</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">torch.fft</a></li>
<li class="toctree-l1"><a class="reference internal" href="futures.html">torch.futures</a></li>
<li class="toctree-l1"><a class="reference internal" href="fx.html">torch.fx</a></li>
<li class="toctree-l1"><a class="reference internal" href="hub.html">torch.hub</a></li>
<li class="toctree-l1"><a class="reference internal" href="jit.html">torch.jit</a></li>
<li class="toctree-l1"><a class="reference internal" href="linalg.html">torch.linalg</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch.overrides.html">torch.overrides</a></li>
<li class="toctree-l1"><a class="reference internal" href="profiler.html">torch.profiler</a></li >
<li class="toctree-l1"><a class="reference internal" href="nn.init.html">torch.nn.init</a></li>
<li class="toctree-l1"><a class="reference internal" href="onnx.html">torch.onnx</a></li>
<li class="toctree-l1"><a class="reference internal" href="optim.html">torch.optim</a></li>
<li class="toctree-l1"><a class="reference internal" href="complex_numbers.html">Complex Numbers</a></li>
<li class="toctree-l1"><a class="reference internal" href="ddp_comm_hooks.html">DDP Communication Hooks</a></li>
<li class="toctree-l1"><a class="reference internal" href="pipeline.html">Pipeline Parallelism</a></li>
<li class="toctree-l1"><a class="reference internal" href="quantization.html">Quantization</a></li>
<li class="toctree-l1"><a class="reference internal" href="rpc.html">Distributed RPC Framework</a></li>
<li class="toctree-l1"><a class="reference internal" href="random.html">torch.random</a></li>
<li class="toctree-l1"><a class="reference internal" href="sparse.html">torch.sparse</a></li>
<li class="toctree-l1"><a class="reference internal" href="storage.html">torch.Storage</a></li>
<li class="toctree-l1"><a class="reference internal" href="benchmark_utils.html">torch.utils.benchmark</a></li>
<li class="toctree-l1"><a class="reference internal" href="bottleneck.html">torch.utils.bottleneck</a></li>
<li class="toctree-l1"><a class="reference internal" href="checkpoint.html">torch.utils.checkpoint</a></li>
<li class="toctree-l1"><a class="reference internal" href="cpp_extension.html">torch.utils.cpp_extension</a></li>
<li class="toctree-l1"><a class="reference internal" href="data.html">torch.utils.data</a></li>
<li class="toctree-l1"><a class="reference internal" href="dlpack.html">torch.utils.dlpack</a></li>
<li class="toctree-l1"><a class="reference internal" href="mobile_optimizer.html">torch.utils.mobile_optimizer</a></li>
<li class="toctree-l1"><a class="reference internal" href="model_zoo.html">torch.utils.model_zoo</a></li>
<li class="toctree-l1"><a class="reference internal" href="tensorboard.html">torch.utils.tensorboard</a></li>
<li class="toctree-l1"><a class="reference internal" href="type_info.html">Type Info</a></li>
<li class="toctree-l1"><a class="reference internal" href="named_tensor.html">Named Tensors</a></li>
<li class="toctree-l1"><a class="reference internal" href="name_inference.html">Named Tensors operator coverage</a></li>
<li class="toctree-l1"><a class="reference internal" href="__config__.html">torch.__config__</a></li>
</ul>
<p class="caption"><span class="caption-text">Libraries</span></p>
<ul>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/audio/stable">torchaudio</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/text/stable">torchtext</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/vision/stable">torchvision</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/elastic/">TorchElastic</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/serve">TorchServe</a></li>
<li class="toctree-l1"><a class="reference external" href="http://pytorch.org/xla/">PyTorch on XLA Devices</a></li>
</ul>
<p class="caption"><span class="caption-text">Community</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="community/contribution_guide.html">PyTorch Contribution Guide</a></li>
<li class="toctree-l1"><a class="reference internal" href="community/governance.html">PyTorch Governance</a></li>
<li class="toctree-l1"><a class="reference internal" href="community/persons_of_interest.html">PyTorch Governance | Persons of Interest</a></li>
</ul>
</div>
</div>
</nav>
<div class="pytorch-container">
<div class="pytorch-page-level-bar" id="pytorch-page-level-bar">
<div class="pytorch-breadcrumbs-wrapper">
<div role="navigation" aria-label="breadcrumbs navigation">
<ul class="pytorch-breadcrumbs">
<li>
<a href="index.html">
Docs
</a> >
</li>
<li>torch.fft</li>
<li class="pytorch-breadcrumbs-aside">
<a href="_sources/fft.rst.txt" rel="nofollow"><img src="_static/images/view-page-source-icon.svg"></a>
</li>
</ul>
</div>
</div>
<div class="pytorch-shortcuts-wrapper" id="pytorch-shortcuts-wrapper">
Shortcuts
</div>
</div>
<section data-toggle="wy-nav-shift" id="pytorch-content-wrap" class="pytorch-content-wrap">
<div class="pytorch-content-left">
<div class="rst-content">
<div role="main" class="main-content" itemscope="itemscope" itemtype="http://schema.org/Article">
<article itemprop="articleBody" id="pytorch-article" class="pytorch-article">
<div class="section" id="torch-fft">
<h1>torch.fft<a class="headerlink" href="#torch-fft" title="Permalink to this headline">¶</a></h1>
<p>Discrete Fourier transforms and related functions.</p>
<div class="section" id="fast-fourier-transforms">
<h2>Fast Fourier Transforms<a class="headerlink" href="#fast-fourier-transforms" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="torch.fft.fft">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">fft</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">n=None</em>, <em class="sig-param">dim=-1</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.fft" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the one dimensional discrete Fourier transform of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The Fourier domain representation of any real signal satisfies the
Hermitian property: <cite>X[i] = conj(X[-i])</cite>. This function always returns both
the positive and negative frequency terms even though, for real inputs, the
negative frequencies are redundant. <a class="reference internal" href="#torch.fft.rfft" title="torch.fft.rfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft()</span></code></a> returns the
more compact one-sided representation where only the positive frequencies
are returned.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>n</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>, </em><em>optional</em>) – Signal length. If given, the input will either be zero-padded
or trimmed to this length before computing the FFT.</p></li>
<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>, </em><em>optional</em>) – The dimension along which to take the one dimensional FFT.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the forward transform
(<a class="reference internal" href="#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the FFT orthonormal)</p></li>
</ul>
<p>Calling the backward transform (<a class="reference internal" href="#torch.fft.ifft" title="torch.fft.ifft"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="#torch.fft.ifft" title="torch.fft.ifft"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (no normalization).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">t</span>
<span class="go">tensor([0, 1, 2, 3])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="go">tensor([ 6.+0.j, -2.+2.j, -2.+0.j, -2.-2.j])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">tensor</span><span class="p">([</span><span class="mf">0.</span><span class="o">+</span><span class="mf">1.</span><span class="n">j</span><span class="p">,</span> <span class="mf">2.</span><span class="o">+</span><span class="mf">3.</span><span class="n">j</span><span class="p">,</span> <span class="mf">4.</span><span class="o">+</span><span class="mf">5.</span><span class="n">j</span><span class="p">,</span> <span class="mf">6.</span><span class="o">+</span><span class="mf">7.</span><span class="n">j</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="go">tensor([12.+16.j, -8.+0.j, -4.-4.j, 0.-8.j])</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.ifft">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">ifft</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">n=None</em>, <em class="sig-param">dim=-1</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.ifft" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the one dimensional inverse discrete Fourier transform of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>n</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>, </em><em>optional</em>) – Signal length. If given, the input will either be zero-padded
or trimmed to this length before computing the IFFT.</p></li>
<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>, </em><em>optional</em>) – The dimension along which to take the one dimensional IFFT.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the backward transform
(<a class="reference internal" href="#torch.fft.ifft" title="torch.fft.ifft"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the IFFT orthonormal)</p></li>
</ul>
<p>Calling the forward transform (<a class="reference internal" href="#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="#torch.fft.ifft" title="torch.fft.ifft"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code>).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span> <span class="mf">6.</span><span class="o">+</span><span class="mf">0.</span><span class="n">j</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="o">+</span><span class="mf">2.</span><span class="n">j</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="o">+</span><span class="mf">0.</span><span class="n">j</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="o">-</span><span class="mf">2.</span><span class="n">j</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">ifft</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="go">tensor([0.+0.j, 1.+0.j, 2.+0.j, 3.+0.j])</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.fft2">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">fft2</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">s=None</em>, <em class="sig-param">dim=(-2</em>, <em class="sig-param">-1)</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.fft2" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the 2 dimensional discrete Fourier transform of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.
Equivalent to <a class="reference internal" href="#torch.fft.fftn" title="torch.fft.fftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">fftn()</span></code></a> but FFTs only the last two dimensions by default.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The Fourier domain representation of any real signal satisfies the
Hermitian property: <code class="docutils literal notranslate"><span class="pre">X[i,</span> <span class="pre">j]</span> <span class="pre">=</span> <span class="pre">conj(X[-i,</span> <span class="pre">-j])</span></code>. This
function always returns all positive and negative frequency terms even
though, for real inputs, half of these values are redundant.
<a class="reference internal" href="#torch.fft.rfft2" title="torch.fft.rfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft2()</span></code></a> returns the more compact one-sided representation
where only the positive frequencies of the last dimension are returned.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>s</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Signal size in the transformed dimensions.
If given, each dimension <code class="docutils literal notranslate"><span class="pre">dim[i]</span></code> will either be zero-padded or
trimmed to the length <code class="docutils literal notranslate"><span class="pre">s[i]</span></code> before computing the FFT.
If a length <code class="docutils literal notranslate"><span class="pre">-1</span></code> is specified, no padding is done in that dimension.
Default: <code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">=</span> <span class="pre">[input.size(d)</span> <span class="pre">for</span> <span class="pre">d</span> <span class="pre">in</span> <span class="pre">dim]</span></code></p></li>
<li><p><strong>dim</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Dimensions to be transformed.
Default: last two dimensions.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the forward transform
(<a class="reference internal" href="#torch.fft.fft2" title="torch.fft.fft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft2()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the FFT orthonormal)</p></li>
</ul>
<p>Where <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">=</span> <span class="pre">prod(s)</span></code> is the logical FFT size.
Calling the backward transform (<a class="reference internal" href="#torch.fft.ifft2" title="torch.fft.ifft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft2()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code>
between the two transforms. This is required to make
<a class="reference internal" href="#torch.fft.ifft2" title="torch.fft.ifft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft2()</span></code></a> the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (no normalization).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">complex64</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">fft2</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft2</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
</pre></div>
</div>
<p>The discrete Fourier transform is separable, so <a class="reference internal" href="#torch.fft.fft2" title="torch.fft.fft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft2()</span></code></a>
here is equivalent to two one-dimensional <a class="reference internal" href="#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a> calls:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">two_ffts</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">fft2</span><span class="p">,</span> <span class="n">two_ffts</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.ifft2">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">ifft2</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">s=None</em>, <em class="sig-param">dim=(-2</em>, <em class="sig-param">-1)</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.ifft2" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the 2 dimensional inverse discrete Fourier transform of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.
Equivalent to <a class="reference internal" href="#torch.fft.ifftn" title="torch.fft.ifftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifftn()</span></code></a> but IFFTs only the last two dimensions by default.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>s</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Signal size in the transformed dimensions.
If given, each dimension <code class="docutils literal notranslate"><span class="pre">dim[i]</span></code> will either be zero-padded or
trimmed to the length <code class="docutils literal notranslate"><span class="pre">s[i]</span></code> before computing the IFFT.
If a length <code class="docutils literal notranslate"><span class="pre">-1</span></code> is specified, no padding is done in that dimension.
Default: <code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">=</span> <span class="pre">[input.size(d)</span> <span class="pre">for</span> <span class="pre">d</span> <span class="pre">in</span> <span class="pre">dim]</span></code></p></li>
<li><p><strong>dim</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Dimensions to be transformed.
Default: last two dimensions.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the backward transform
(<a class="reference internal" href="#torch.fft.ifft2" title="torch.fft.ifft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft2()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the IFFT orthonormal)</p></li>
</ul>
<p>Where <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">=</span> <span class="pre">prod(s)</span></code> is the logical IFFT size.
Calling the forward transform (<a class="reference internal" href="#torch.fft.fft2" title="torch.fft.fft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft2()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="#torch.fft.ifft2" title="torch.fft.ifft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft2()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code>).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">complex64</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">ifft2</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">ifft2</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
</pre></div>
</div>
<p>The discrete Fourier transform is separable, so <a class="reference internal" href="#torch.fft.ifft2" title="torch.fft.ifft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft2()</span></code></a>
here is equivalent to two one-dimensional <a class="reference internal" href="#torch.fft.ifft" title="torch.fft.ifft"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft()</span></code></a> calls:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">two_iffts</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">ifft</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">ifft</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">ifft2</span><span class="p">,</span> <span class="n">two_iffts</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.fftn">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">fftn</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">s=None</em>, <em class="sig-param">dim=None</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.fftn" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the N dimensional discrete Fourier transform of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The Fourier domain representation of any real signal satisfies the
Hermitian property: <code class="docutils literal notranslate"><span class="pre">X[i_1,</span> <span class="pre">...,</span> <span class="pre">i_n]</span> <span class="pre">=</span> <span class="pre">conj(X[-i_1,</span> <span class="pre">...,</span> <span class="pre">-i_n])</span></code>. This
function always returns all positive and negative frequency terms even
though, for real inputs, half of these values are redundant.
<a class="reference internal" href="#torch.fft.rfftn" title="torch.fft.rfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfftn()</span></code></a> returns the more compact one-sided representation
where only the positive frequencies of the last dimension are returned.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>s</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Signal size in the transformed dimensions.
If given, each dimension <code class="docutils literal notranslate"><span class="pre">dim[i]</span></code> will either be zero-padded or
trimmed to the length <code class="docutils literal notranslate"><span class="pre">s[i]</span></code> before computing the FFT.
If a length <code class="docutils literal notranslate"><span class="pre">-1</span></code> is specified, no padding is done in that dimension.
Default: <code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">=</span> <span class="pre">[input.size(d)</span> <span class="pre">for</span> <span class="pre">d</span> <span class="pre">in</span> <span class="pre">dim]</span></code></p></li>
<li><p><strong>dim</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Dimensions to be transformed.
Default: all dimensions, or the last <code class="docutils literal notranslate"><span class="pre">len(s)</span></code> dimensions if <code class="xref py py-attr docutils literal notranslate"><span class="pre">s</span></code> is given.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the forward transform
(<a class="reference internal" href="#torch.fft.fftn" title="torch.fft.fftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">fftn()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the FFT orthonormal)</p></li>
</ul>
<p>Where <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">=</span> <span class="pre">prod(s)</span></code> is the logical FFT size.
Calling the backward transform (<a class="reference internal" href="#torch.fft.ifftn" title="torch.fft.ifftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifftn()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code>
between the two transforms. This is required to make
<a class="reference internal" href="#torch.fft.ifftn" title="torch.fft.ifftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifftn()</span></code></a> the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (no normalization).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">complex64</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">fftn</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftn</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
</pre></div>
</div>
<p>The discrete Fourier transform is separable, so <a class="reference internal" href="#torch.fft.fftn" title="torch.fft.fftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">fftn()</span></code></a>
here is equivalent to two one-dimensional <a class="reference internal" href="#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a> calls:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">two_ffts</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">fftn</span><span class="p">,</span> <span class="n">two_ffts</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.ifftn">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">ifftn</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">s=None</em>, <em class="sig-param">dim=None</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.ifftn" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the N dimensional inverse discrete Fourier transform of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>s</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Signal size in the transformed dimensions.
If given, each dimension <code class="docutils literal notranslate"><span class="pre">dim[i]</span></code> will either be zero-padded or
trimmed to the length <code class="docutils literal notranslate"><span class="pre">s[i]</span></code> before computing the IFFT.
If a length <code class="docutils literal notranslate"><span class="pre">-1</span></code> is specified, no padding is done in that dimension.
Default: <code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">=</span> <span class="pre">[input.size(d)</span> <span class="pre">for</span> <span class="pre">d</span> <span class="pre">in</span> <span class="pre">dim]</span></code></p></li>
<li><p><strong>dim</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Dimensions to be transformed.
Default: all dimensions, or the last <code class="docutils literal notranslate"><span class="pre">len(s)</span></code> dimensions if <code class="xref py py-attr docutils literal notranslate"><span class="pre">s</span></code> is given.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the backward transform
(<a class="reference internal" href="#torch.fft.ifftn" title="torch.fft.ifftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifftn()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the IFFT orthonormal)</p></li>
</ul>
<p>Where <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">=</span> <span class="pre">prod(s)</span></code> is the logical IFFT size.
Calling the forward transform (<a class="reference internal" href="#torch.fft.fftn" title="torch.fft.fftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">fftn()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="#torch.fft.ifftn" title="torch.fft.ifftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifftn()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code>).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">complex64</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">ifftn</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">ifftn</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
</pre></div>
</div>
<p>The discrete Fourier transform is separable, so <a class="reference internal" href="#torch.fft.ifftn" title="torch.fft.ifftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifftn()</span></code></a>
here is equivalent to two one-dimensional <a class="reference internal" href="#torch.fft.ifft" title="torch.fft.ifft"><code class="xref py py-func docutils literal notranslate"><span class="pre">ifft()</span></code></a> calls:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">two_iffts</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">ifft</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">ifft</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">ifftn</span><span class="p">,</span> <span class="n">two_iffts</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.rfft">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">rfft</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">n=None</em>, <em class="sig-param">dim=-1</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.rfft" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the one dimensional Fourier transform of real-valued <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.</p>
<p>The FFT of a real signal is Hermitian-symmetric, <code class="docutils literal notranslate"><span class="pre">X[i]</span> <span class="pre">=</span> <span class="pre">conj(X[-i])</span></code> so
the output contains only the positive frequencies below the Nyquist frequency.
To compute the full output, use <a class="reference internal" href="#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the real input tensor</p></li>
<li><p><strong>n</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>, </em><em>optional</em>) – Signal length. If given, the input will either be zero-padded
or trimmed to this length before computing the real FFT.</p></li>
<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>, </em><em>optional</em>) – The dimension along which to take the one dimensional real FFT.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the forward transform
(<a class="reference internal" href="#torch.fft.rfft" title="torch.fft.rfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the FFT orthonormal)</p></li>
</ul>
<p>Calling the backward transform (<a class="reference internal" href="#torch.fft.irfft" title="torch.fft.irfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="#torch.fft.irfft" title="torch.fft.irfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (no normalization).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">t</span>
<span class="go">tensor([0, 1, 2, 3])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="go">tensor([ 6.+0.j, -2.+2.j, -2.+0.j])</span>
</pre></div>
</div>
<p>Compare against the full output from <a class="reference internal" href="#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a>:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="go">tensor([ 6.+0.j, -2.+2.j, -2.+0.j, -2.-2.j])</span>
</pre></div>
</div>
<p>Notice that the symmetric element <code class="docutils literal notranslate"><span class="pre">T[-1]</span> <span class="pre">==</span> <span class="pre">T[1].conj()</span></code> is omitted.
At the Nyquist frequency <code class="docutils literal notranslate"><span class="pre">T[-2]</span> <span class="pre">==</span> <span class="pre">T[2]</span></code> is it’s own symmetric pair,
and therefore must always be real-valued.</p>
</dd></dl>
<dl class="function">
<dt id="torch.fft.irfft">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">irfft</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">n=None</em>, <em class="sig-param">dim=-1</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.irfft" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the inverse of <a class="reference internal" href="#torch.fft.rfft" title="torch.fft.rfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft()</span></code></a>.</p>
<p><code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> is interpreted as a one-sided Hermitian signal in the Fourier
domain, as produced by <a class="reference internal" href="#torch.fft.rfft" title="torch.fft.rfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft()</span></code></a>. By the Hermitian property, the
output will be real-valued.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Some input frequencies must be real-valued to satisfy the Hermitian
property. In these cases the imaginary component will be ignored.
For example, any imaginary component in the zero-frequency term cannot
be represented in a real output and so will always be ignored.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The correct interpretation of the Hermitian input depends on the length of
the original data, as given by <code class="xref py py-attr docutils literal notranslate"><span class="pre">n</span></code>. This is because each input shape
could correspond to either an odd or even length signal. By default, the
signal is assumed to be even length and odd signals will not round-trip
properly. So, it is recommended to always pass the signal length <code class="xref py py-attr docutils literal notranslate"><span class="pre">n</span></code>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor representing a half-Hermitian signal</p></li>
<li><p><strong>n</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>, </em><em>optional</em>) – Output signal length. This determines the length of the
output signal. If given, the input will either be zero-padded or trimmed to this
length before computing the real IFFT.
Defaults to even output: <code class="docutils literal notranslate"><span class="pre">n=2*(input.size(dim)</span> <span class="pre">-</span> <span class="pre">1)</span></code>.</p></li>
<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>, </em><em>optional</em>) – The dimension along which to take the one dimensional real IFFT.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the backward transform
(<a class="reference internal" href="#torch.fft.irfft" title="torch.fft.irfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the real IFFT orthonormal)</p></li>
</ul>
<p>Calling the forward transform (<a class="reference internal" href="#torch.fft.rfft" title="torch.fft.rfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="#torch.fft.irfft" title="torch.fft.irfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code>).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">t</span>
<span class="go">tensor([0, 1, 2, 3, 4])</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">T</span>
<span class="go">tensor([10.0000+0.0000j, -2.5000+3.4410j, -2.5000+0.8123j])</span>
</pre></div>
</div>
<p>Without specifying the output length to <a class="reference internal" href="#torch.fft.irfft" title="torch.fft.irfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft()</span></code></a>, the output
will not round-trip properly because the input is odd-length:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="go">tensor([0.6250, 1.4045, 3.1250, 4.8455])</span>
</pre></div>
</div>
<p>So, it is recommended to always pass the signal length <code class="xref py py-attr docutils literal notranslate"><span class="pre">n</span></code>:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">t</span><span class="o">.</span><span class="n">numel</span><span class="p">())</span>
<span class="go">tensor([0.0000, 1.0000, 2.0000, 3.0000, 4.0000])</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.rfft2">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">rfft2</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">s=None</em>, <em class="sig-param">dim=(-2</em>, <em class="sig-param">-1)</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.rfft2" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the 2-dimensional discrete Fourier transform of real <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.
Equivalent to <a class="reference internal" href="#torch.fft.rfftn" title="torch.fft.rfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfftn()</span></code></a> but FFTs only the last two dimensions by default.</p>
<p>The FFT of a real signal is Hermitian-symmetric, <code class="docutils literal notranslate"><span class="pre">X[i,</span> <span class="pre">j]</span> <span class="pre">=</span> <span class="pre">conj(X[-i,</span> <span class="pre">-j])</span></code>,
so the full <a class="reference internal" href="#torch.fft.fft2" title="torch.fft.fft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft2()</span></code></a> output contains redundant information.
<a class="reference internal" href="#torch.fft.rfft2" title="torch.fft.rfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft2()</span></code></a> instead omits the negative frequencies in the last
dimension.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>s</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Signal size in the transformed dimensions.
If given, each dimension <code class="docutils literal notranslate"><span class="pre">dim[i]</span></code> will either be zero-padded or
trimmed to the length <code class="docutils literal notranslate"><span class="pre">s[i]</span></code> before computing the real FFT.
If a length <code class="docutils literal notranslate"><span class="pre">-1</span></code> is specified, no padding is done in that dimension.
Default: <code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">=</span> <span class="pre">[input.size(d)</span> <span class="pre">for</span> <span class="pre">d</span> <span class="pre">in</span> <span class="pre">dim]</span></code></p></li>
<li><p><strong>dim</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Dimensions to be transformed.
Default: last two dimensions.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the forward transform
(<a class="reference internal" href="#torch.fft.rfft2" title="torch.fft.rfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft2()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the real FFT orthonormal)</p></li>
</ul>
<p>Where <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">=</span> <span class="pre">prod(s)</span></code> is the logical FFT size.
Calling the backward transform (<a class="reference internal" href="#torch.fft.irfft2" title="torch.fft.irfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft2()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="#torch.fft.irfft2" title="torch.fft.irfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft2()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (no normalization).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">rfft2</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft2</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">rfft2</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="go">torch.Size([10, 6])</span>
</pre></div>
</div>
<p>Compared against the full output from <a class="reference internal" href="#torch.fft.fft2" title="torch.fft.fft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft2()</span></code></a>, we have all
elements up to the Nyquist frequency.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">fft2</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft2</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">fft2</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="p">:</span><span class="mi">6</span><span class="p">],</span> <span class="n">rfft2</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
<p>The discrete Fourier transform is separable, so <a class="reference internal" href="#torch.fft.rfft2" title="torch.fft.rfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft2()</span></code></a>
here is equivalent to a combination of <a class="reference internal" href="#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a> and
<a class="reference internal" href="#torch.fft.rfft" title="torch.fft.rfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft()</span></code></a>:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">two_ffts</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">rfft2</span><span class="p">,</span> <span class="n">two_ffts</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.irfft2">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">irfft2</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">s=None</em>, <em class="sig-param">dim=(-2</em>, <em class="sig-param">-1)</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.irfft2" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the inverse of <a class="reference internal" href="#torch.fft.rfft2" title="torch.fft.rfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft2()</span></code></a>.
Equivalent to <a class="reference internal" href="#torch.fft.irfftn" title="torch.fft.irfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfftn()</span></code></a> but IFFTs only the last two dimensions by default.</p>
<p><code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> is interpreted as a one-sided Hermitian signal in the Fourier
domain, as produced by <a class="reference internal" href="#torch.fft.rfft2" title="torch.fft.rfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft2()</span></code></a>. By the Hermitian property, the
output will be real-valued.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Some input frequencies must be real-valued to satisfy the Hermitian
property. In these cases the imaginary component will be ignored.
For example, any imaginary component in the zero-frequency term cannot
be represented in a real output and so will always be ignored.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The correct interpretation of the Hermitian input depends on the length of
the original data, as given by <code class="xref py py-attr docutils literal notranslate"><span class="pre">s</span></code>. This is because each input shape
could correspond to either an odd or even length signal. By default, the
signal is assumed to be even length and odd signals will not round-trip
properly. So, it is recommended to always pass the signal shape <code class="xref py py-attr docutils literal notranslate"><span class="pre">s</span></code>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>s</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Signal size in the transformed dimensions.
If given, each dimension <code class="docutils literal notranslate"><span class="pre">dim[i]</span></code> will either be zero-padded or
trimmed to the length <code class="docutils literal notranslate"><span class="pre">s[i]</span></code> before computing the real FFT.
If a length <code class="docutils literal notranslate"><span class="pre">-1</span></code> is specified, no padding is done in that dimension.
Defaults to even output in the last dimension:
<code class="docutils literal notranslate"><span class="pre">s[-1]</span> <span class="pre">=</span> <span class="pre">2*(input.size(dim[-1])</span> <span class="pre">-</span> <span class="pre">1)</span></code>.</p></li>
<li><p><strong>dim</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Dimensions to be transformed.
The last dimension must be the half-Hermitian compressed dimension.
Default: last two dimensions.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the backward transform
(<a class="reference internal" href="#torch.fft.irfft2" title="torch.fft.irfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft2()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the real IFFT orthonormal)</p></li>
</ul>
<p>Where <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">=</span> <span class="pre">prod(s)</span></code> is the logical IFFT size.
Calling the forward transform (<a class="reference internal" href="#torch.fft.rfft2" title="torch.fft.rfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft2()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="#torch.fft.irfft2" title="torch.fft.irfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft2()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code>).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">9</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft2</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
</pre></div>
</div>
<p>Without specifying the output length to <a class="reference internal" href="#torch.fft.irfft2" title="torch.fft.irfft2"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfft2()</span></code></a>, the output
will not round-trip properly because the input is odd-length in the last
dimension:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft2</span><span class="p">(</span><span class="n">T</span><span class="p">)</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="go">torch.Size([10, 10])</span>
</pre></div>
</div>
<p>So, it is recommended to always pass the signal shape <code class="xref py py-attr docutils literal notranslate"><span class="pre">s</span></code>.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">roundtrip</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft2</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">t</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
<span class="gp">>>> </span><span class="n">roundtrip</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="go">torch.Size([10, 9])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">roundtrip</span><span class="p">,</span> <span class="n">t</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.rfftn">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">rfftn</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">s=None</em>, <em class="sig-param">dim=None</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.rfftn" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the N-dimensional discrete Fourier transform of real <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>.</p>
<p>The FFT of a real signal is Hermitian-symmetric,
<code class="docutils literal notranslate"><span class="pre">X[i_1,</span> <span class="pre">...,</span> <span class="pre">i_n]</span> <span class="pre">=</span> <span class="pre">conj(X[-i_1,</span> <span class="pre">...,</span> <span class="pre">-i_n])</span></code> so the full
<a class="reference internal" href="#torch.fft.fftn" title="torch.fft.fftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">fftn()</span></code></a> output contains redundant information.
<a class="reference internal" href="#torch.fft.rfftn" title="torch.fft.rfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfftn()</span></code></a> instead omits the negative frequencies in the
last dimension.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>s</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Signal size in the transformed dimensions.
If given, each dimension <code class="docutils literal notranslate"><span class="pre">dim[i]</span></code> will either be zero-padded or
trimmed to the length <code class="docutils literal notranslate"><span class="pre">s[i]</span></code> before computing the real FFT.
If a length <code class="docutils literal notranslate"><span class="pre">-1</span></code> is specified, no padding is done in that dimension.
Default: <code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">=</span> <span class="pre">[input.size(d)</span> <span class="pre">for</span> <span class="pre">d</span> <span class="pre">in</span> <span class="pre">dim]</span></code></p></li>
<li><p><strong>dim</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Dimensions to be transformed.
Default: all dimensions, or the last <code class="docutils literal notranslate"><span class="pre">len(s)</span></code> dimensions if <code class="xref py py-attr docutils literal notranslate"><span class="pre">s</span></code> is given.</p></li>
<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.9)"><em>str</em></a><em>, </em><em>optional</em>) – <p>Normalization mode. For the forward transform
(<a class="reference internal" href="#torch.fft.rfftn" title="torch.fft.rfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfftn()</span></code></a>), these correspond to:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">"forward"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/n</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"backward"</span></code> - no normalization</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"ortho"</span></code> - normalize by <code class="docutils literal notranslate"><span class="pre">1/sqrt(n)</span></code> (making the real FFT orthonormal)</p></li>
</ul>
<p>Where <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">=</span> <span class="pre">prod(s)</span></code> is the logical FFT size.
Calling the backward transform (<a class="reference internal" href="#torch.fft.irfftn" title="torch.fft.irfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfftn()</span></code></a>) with the same
normalization mode will apply an overall normalization of <code class="docutils literal notranslate"><span class="pre">1/n</span></code> between
the two transforms. This is required to make <a class="reference internal" href="#torch.fft.irfftn" title="torch.fft.irfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">irfftn()</span></code></a>
the exact inverse.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">"backward"</span></code> (no normalization).</p>
</p></li>
</ul>
</dd>
</dl>
<p class="rubric">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">t</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">rfftn</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfftn</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">rfftn</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
<span class="go">torch.Size([10, 6])</span>
</pre></div>
</div>
<p>Compared against the full output from <a class="reference internal" href="#torch.fft.fftn" title="torch.fft.fftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">fftn()</span></code></a>, we have all
elements up to the Nyquist frequency.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">fftn</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftn</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">fftn</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="p">:</span><span class="mi">6</span><span class="p">],</span> <span class="n">rfftn</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
<p>The discrete Fourier transform is separable, so <a class="reference internal" href="#torch.fft.rfftn" title="torch.fft.rfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfftn()</span></code></a>
here is equivalent to a combination of <a class="reference internal" href="#torch.fft.fft" title="torch.fft.fft"><code class="xref py py-func docutils literal notranslate"><span class="pre">fft()</span></code></a> and
<a class="reference internal" href="#torch.fft.rfft" title="torch.fft.rfft"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfft()</span></code></a>:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">two_ffts</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">rfftn</span><span class="p">,</span> <span class="n">two_ffts</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="torch.fft.irfftn">
<code class="sig-prename descclassname">torch.fft.</code><code class="sig-name descname">irfftn</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">s=None</em>, <em class="sig-param">dim=None</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.fft.irfftn" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the inverse of <a class="reference internal" href="#torch.fft.rfftn" title="torch.fft.rfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfftn()</span></code></a>.</p>
<p><code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> is interpreted as a one-sided Hermitian signal in the Fourier
domain, as produced by <a class="reference internal" href="#torch.fft.rfftn" title="torch.fft.rfftn"><code class="xref py py-func docutils literal notranslate"><span class="pre">rfftn()</span></code></a>. By the Hermitian property, the
output will be real-valued.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Some input frequencies must be real-valued to satisfy the Hermitian
property. In these cases the imaginary component will be ignored.
For example, any imaginary component in the zero-frequency term cannot
be represented in a real output and so will always be ignored.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The correct interpretation of the Hermitian input depends on the length of
the original data, as given by <code class="xref py py-attr docutils literal notranslate"><span class="pre">s</span></code>. This is because each input shape
could correspond to either an odd or even length signal. By default, the
signal is assumed to be even length and odd signals will not round-trip
properly. So, it is recommended to always pass the signal shape <code class="xref py py-attr docutils literal notranslate"><span class="pre">s</span></code>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the input tensor</p></li>
<li><p><strong>s</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>]</em><em>, </em><em>optional</em>) – Signal size in the transformed dimensions.