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bundles / numpy 2.4.3 / numpy / fft / fft

_ArrayFunctionDispatcher

numpy.fft:fft

source: /numpy/fft/_pocketfft.py :120

Signature

def   fft ( a ,  n = None ,  axis = -1 ,  norm = None ,  out = None )

Summary

Compute the one-dimensional discrete Fourier Transform.

Extended Summary

This function computes the one-dimensional n-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm [CT].

Parameters

a : array_like

Input array, can be complex.

n : int, optional

Length of the transformed axis of the output. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.

axis : int, optional

Axis over which to compute the FFT. If not given, the last axis is used.

norm : {"backward", "ortho", "forward"}, optional

Normalization mode (see numpy.fft). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.

out : complex ndarray, optional

If provided, the result will be placed in this array. It should be of the appropriate shape and dtype.

Returns

out : complex ndarray

The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified.

Raises

: IndexError

If axis is not a valid axis of a.

Notes

FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform (DFT) can be calculated efficiently, by using symmetries in the calculated terms. The symmetry is highest when n is a power of 2, and the transform is therefore most efficient for these sizes.

The DFT is defined, with the conventions used in this implementation, in the documentation for the numpy.fft module.

Examples

import numpy as np
✓
np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8))
✗
In this example, real input has an FFT which is Hermitian, i.e., symmetric in the real part and anti-symmetric in the imaginary part, as described in the `numpy.fft` documentation: 
import matplotlib.pyplot as plt
t = np.arange(256)
sp = np.fft.fft(np.sin(t))
freq = np.fft.fftfreq(t.shape[-1])
_ = plt.plot(freq, sp.real, freq, sp.imag)
plt.show()
✓
fig-deea99106d036e8b.png

See also

fft2

The two-dimensional FFT.

fftfreq

Frequency bins for given FFT parameters.

fftn

The n-dimensional FFT.

ifft

The inverse of fft.

numpy.fft

for definition of the DFT and conventions used.

rfftn

The n-dimensional FFT of real input.

Aliases

  • numpy.fft.fft