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).
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.
Input array, can be complex.
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 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.
Normalization mode (see fft
). Default is "backward".
If True, the contents of x can be destroyed; the default is False. See fft
for more details.
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.
This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
If s and :None:None:`axes` have different length.
If an element of :None:None:`axes` is larger than than the number of axes of x.
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.
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.
>>> 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()
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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