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<section id="numpy-blackman">
<h1>numpy.blackman<a class="headerlink" href="#numpy-blackman" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="numpy.blackman">
<span class="sig-prename descclassname"><span class="pre">numpy.</span></span><span class="sig-name descname"><span class="pre">blackman</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">M</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/main/numpy/lib/_function_base_impl.py#L3056-L3153"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#numpy.blackman" title="Link to this definition">#</a></dt>
<dd><p>Return the Blackman window.</p>
<p>The Blackman window is a taper formed by using the first three
terms of a summation of cosines. It was designed to have close to the
minimal leakage possible. It is close to optimal, only slightly worse
than a Kaiser window.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>M</strong><span class="classifier">int</span></dt><dd><p>Number of points in the output window. If zero or less, an empty
array is returned.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray</span></dt><dd><p>The window, with the maximum value normalized to one (the value one
appears only if the number of samples is odd).</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.bartlett.html#numpy.bartlett" title="numpy.bartlett"><code class="xref py py-obj docutils literal notranslate"><span class="pre">bartlett</span></code></a>, <a class="reference internal" href="numpy.hamming.html#numpy.hamming" title="numpy.hamming"><code class="xref py py-obj docutils literal notranslate"><span class="pre">hamming</span></code></a>, <a class="reference internal" href="numpy.hanning.html#numpy.hanning" title="numpy.hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">hanning</span></code></a>, <a class="reference internal" href="numpy.kaiser.html#numpy.kaiser" title="numpy.kaiser"><code class="xref py py-obj docutils literal notranslate"><span class="pre">kaiser</span></code></a></dt><dd></dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The Blackman window is defined as</p>
<div class="math notranslate nohighlight">
\[w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M)\]</div>
<p>Most references to the Blackman window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
“removing the foot”, i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function. It is known as a
“near optimal” tapering function, almost as good (by some measures)
as the kaiser window.</p>
<p class="rubric">References</p>
<p>Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,
Dover Publications, New York.</p>
<p>Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.
Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.</p>
<p class="rubric">Examples</p>
<div class="try_examples_outer_container docutils container" id="5c259706-671d-436c-a4a3-303faca9a1b0">
<div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesShowIframe('5c259706-671d-436c-a4a3-303faca9a1b0','4d6639b8-8f3b-4c4f-9238-070145c70941','3c2b7842-ab2e-400d-aa6f-3bcc7958c90c','../../lite/tree/../notebooks/index.html?path=20166e40_56b1_44ae_a4f8_35f95122b43a.ipynb','None')">Try it in your browser!</button></div><div class="try_examples_content docutils container">
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">blackman</span><span class="p">(</span><span class="mi">12</span><span class="p">)</span>
<span class="go">array([-1.38777878e-17, 3.26064346e-02, 1.59903635e-01, # may vary</span>
<span class="go"> 4.14397981e-01, 7.36045180e-01, 9.67046769e-01,</span>
<span class="go"> 9.67046769e-01, 7.36045180e-01, 4.14397981e-01,</span>
<span class="go"> 1.59903635e-01, 3.26064346e-02, -1.38777878e-17])</span>
</pre></div>
</div>
<p>Plot the window and the frequency response.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">numpy.fft</span><span class="w"> </span><span class="kn">import</span> <span class="n">fft</span><span class="p">,</span> <span class="n">fftshift</span>
<span class="n">window</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">blackman</span><span class="p">(</span><span class="mi">51</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">window</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Blackman window"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"Amplitude"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"Sample"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> <span class="c1"># doctest: +SKIP</span>
</pre></div>
</div>
<figure class="align-default">
<img alt="../../_images/numpy-blackman-1_00_00.png" class="plot-directive" src="../../_images/numpy-blackman-1_00_00.png" />
</figure>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">A</span> <span class="o">=</span> <span class="n">fft</span><span class="p">(</span><span class="n">window</span><span class="p">,</span> <span class="mi">2048</span><span class="p">)</span> <span class="o">/</span> <span class="mf">25.5</span>
<span class="n">mag</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">fftshift</span><span class="p">(</span><span class="n">A</span><span class="p">))</span>
<span class="n">freq</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">A</span><span class="p">))</span>
<span class="k">with</span> <span class="n">np</span><span class="o">.</span><span class="n">errstate</span><span class="p">(</span><span class="n">divide</span><span class="o">=</span><span class="s1">'ignore'</span><span class="p">,</span> <span class="n">invalid</span><span class="o">=</span><span class="s1">'ignore'</span><span class="p">):</span>
<span class="n">response</span> <span class="o">=</span> <span class="mi">20</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log10</span><span class="p">(</span><span class="n">mag</span><span class="p">)</span>
<span class="n">response</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="n">response</span><span class="p">,</span> <span class="o">-</span><span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">freq</span><span class="p">,</span> <span class="n">response</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Frequency response of Blackman window"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"Magnitude [dB]"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"Normalized frequency [cycles per sample]"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'tight'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
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