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bundles / numpy 2.4.4 / numpy / fft / fftn

_ArrayFunctionDispatcher

numpy.fft:fftn

source: /numpy/fft/_pocketfft.py :755

Signature

def   fftn ( a ,  s = None ,  axes = None ,  norm = None ,  out = None )

Summary

Compute the N-dimensional discrete Fourier Transform.

Extended Summary

This function computes the N-dimensional discrete Fourier Transform over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT).

Parameters

a : array_like

Input array, can be complex.

s : sequence of ints, optional

Shape (length of each transformed axis) of the output (s[0] refers to axis 0, s[1] to axis 1, etc.). This corresponds to n for fft(x, n). Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros.

If s is not given, the shape of the input along the axes specified by axes is used.

axes : sequence of ints, optional

Axes over which to compute the FFT. If not given, the last len(s) axes are used, or all axes if s is also not specified. Repeated indices in axes means that the transform over that axis is performed multiple times.

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 for all axes (and hence is incompatible with passing in all but the trivial s).

Returns

out : complex ndarray

The truncated or zero-padded input, transformed along the axes indicated by axes, or by a combination of s and a, as explained in the parameters section above.

Raises

: ValueError

If s and axes have different length.

: IndexError

If an element of axes is larger than than the number of axes of a.

Notes

The output, analogously to fft, contains the term for zero frequency in the low-order corner of all axes, the positive frequency terms in the first half of all axes, the term for the Nyquist frequency in the middle of all axes and the negative frequency terms in the second half of all axes, in order of decreasingly negative frequency.

See numpy.fft for details, definitions and conventions used.

Examples

import numpy as np
a = np.mgrid[:3, :3, :3][0]
✓
np.fft.fftn(a, axes=(1, 2))
np.fft.fftn(a, (2, 2), axes=(0, 1))
✗
import matplotlib.pyplot as plt
[X, Y] = np.meshgrid(2 * np.pi * np.arange(200) / 12,
                     2 * np.pi * np.arange(200) / 34)
S = np.sin(X) + np.cos(Y) + np.random.uniform(0, 1, X.shape)
FS = np.fft.fftn(S)
plt.imshow(np.log(np.abs(np.fft.fftshift(FS))**2))
plt.show()
✓
fig-1103b227e2bf4845.png

See also

fft

The one-dimensional FFT, with definitions and conventions used.

fft2

The two-dimensional FFT.

fftshift

Shifts zero-frequency terms to centre of array

ifftn

The inverse of fftn, the inverse n-dimensional FFT.

numpy.fft

Overall view of discrete Fourier transforms, with definitions and conventions used.

rfftn

The n-dimensional FFT of real input.

Aliases

  • numpy.fft.fftn

Referenced by

This package