scipy.fft() in Python

scipy.fft() method in Python computes the Fast Fourier Transform (FFT) of a 1D array, converting a time-domain signal into its frequency-domain form. If no parameters are provided, it uses default settings.

Fast Fourier Transformation Formula:

y[k] = \sum_{n=0}^{N-1} e^{-2\pi j \frac{kn}{N}} x[n]

Where:

• 𝑥 [ 𝑛 ] : input time-domain signal
• 𝑁: number of points
• 𝑗: imaginary unit

Example:

import numpy as np
from scipy.fft import fft

x = np.array([1, 2, 3, 4])
res = fft(x)
print(res)

Output

[10.-0.j -2.+2.j -2.-0.j -2.-2.j]

Explanation: This performs the FFT on a real-valued signal [1, 2, 3, 4]. The output is a complex array representing frequency components.

Syntax of scipy.fft()

scipy.fft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None)

Parameters:

Returns: A NumPy array of complex numbers representing the frequency components of the input signal.

Exceptions:

• ValueError: If input is not array-like or incompatible with FFT computation.
• TypeError: If parameters are passed incorrectly.

Examples

Example 1: Use zero-padding with n parameter

import numpy as np
from scipy.fft import fft

x = np.array([1, 2, 3, 4])
res = fft(x, n=8)
print(res)

Output

[10. -0.j -0.41421356-7.24264069j -2. +2.j
2.41421356-1.24264069j -2. -0.j 2.41421356+1.24264069j
-2. -2.j -0.41421356+7.24264069j]

Explanation: By specifying n=8, the input is zero-padded to a length of 8 before applying FFT.

Example 2: Apply FFT along a specific axis of a 2D array

import numpy as np
from scipy.fft import fft

x = np.array([[1, 2], [3, 4]])
res = fft(x, axis=0)
print(res)

Output

[[ 4.-0.j 6.-0.j]
[-2.-0.j -2.-0.j]]

Explanation: FFT is computed column-wise (i.e., along axis 0) for each column in the 2D array.

Related Articles

• scipy.ifft() method
• numpy.fft.fft()
• scipy.fftpack