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

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.

Parameters

x : 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 :None:None:`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.

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

Normalization mode (see fft ). Default is "backward".

overwrite_x : bool, optional

If True, the contents of x can be destroyed; the default is False. See fft for more details.

workers : int, optional

Maximum number of workers to use for parallel computation. If negative, the value wraps around from os.cpu_count() . See ~scipy.fft.fft for more details.

plan : object, optional

This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.

versionadded

Raises

ValueError

If s and :None:None:`axes` have different length.

IndexError

If an element of :None:None:`axes` is larger than than the number of axes of x.

Returns

out : complex ndarray

The truncated or zero-padded input, transformed along the axes indicated by :None:None:`axes`, or by a combination of s and x, as explained in the parameters section above.

Compute the N-D discrete Fourier Transform.

See Also

fft

The 1-D FFT, with definitions and conventions used.

fft2

The 2-D FFT.

fftshift

Shifts zero-frequency terms to centre of array.

ifftn

The inverse of :None:None:`fftn`, the inverse N-D FFT.

rfftn

The N-D FFT of real input.

Examples

>>> import scipy.fft
... x = np.mgrid[:3, :3, :3][0]
... scipy.fft.fftn(x, axes=(1, 2)) array([[[ 0.+0.j, 0.+0.j, 0.+0.j], # may vary [ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]], [[ 9.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]], [[18.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]]])
>>> scipy.fft.fftn(x, (2, 2), axes=(0, 1))
array([[[ 2.+0.j,  2.+0.j,  2.+0.j], # may vary
        [ 0.+0.j,  0.+0.j,  0.+0.j]],
       [[-2.+0.j, -2.+0.j, -2.+0.j],
        [ 0.+0.j,  0.+0.j,  0.+0.j]]])
>>> import matplotlib.pyplot as plt
... rng = np.random.default_rng()
... [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) + rng.uniform(0, 1, X.shape)
... FS = scipy.fft.fftn(S)
... plt.imshow(np.log(np.abs(scipy.fft.fftshift(FS))**2)) <matplotlib.image.AxesImage object at 0x...>
>>> plt.show()
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.fft._basic.rfftn scipy.fft._basic.rfft scipy.fft._basic.fft scipy.fft._basic.ifftn scipy.fft._basic.ihfftn scipy.fft._basic.fft2

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GitHub : /scipy/fft/_basic.py#615
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