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Module « scipy.fft »

Fonction fftn - module scipy.fft

Signature de la fonction fftn

def fftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *, plan=None) 

Description

help(scipy.fft.fftn)

Compute the N-D discrete Fourier Transform.

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).

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 `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 :func:`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 :func:`~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:: 1.5.0

Returns
-------
out : complex ndarray
    The truncated or zero-padded input, transformed along the axes
    indicated by `axes`, or by a combination of `s` and `x`,
    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 the number of axes of `x`.

See Also
--------
ifftn : The inverse of `fftn`, the inverse N-D FFT.
fft : The 1-D FFT, with definitions and conventions used.
rfftn : The N-D FFT of real input.
fft2 : The 2-D FFT.
fftshift : Shifts zero-frequency terms to centre of array.

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.

Examples
--------
>>> import scipy.fft
>>> import numpy as np
>>> 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()

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