Vous êtes un professionnel et vous avez besoin d'une formation ? Sensibilisation à
l'Intelligence Artificielle Voir le programme détaillé

Module « numpy.fft »

Fonction fftn - module numpy.fft

Signature de la fonction fftn

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

Description

help(numpy.fft.fftn)

Compute the N-dimensional discrete Fourier Transform.

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.

    .. versionchanged:: 2.0

        If it is ``-1``, the whole input is used (no padding/trimming).

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

    .. deprecated:: 2.0

        If `s` is not ``None``, `axes` must not be ``None`` either.

    .. deprecated:: 2.0

        `s` must contain only ``int`` s, not ``None`` values. ``None``
        values currently mean that the default value for ``n`` is used
        in the corresponding 1-D transform, but this behaviour is
        deprecated.

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.

    .. deprecated:: 2.0

        If `s` is specified, the corresponding `axes` to be transformed
        must be explicitly specified too.

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.

    .. versionadded:: 1.20.0

        The "backward", "forward" values were added.

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``).

    .. versionadded:: 2.0.0

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

See Also
--------
numpy.fft : Overall view of discrete Fourier transforms, with definitions
    and conventions used.
ifftn : The inverse of `fftn`, the inverse *n*-dimensional FFT.
fft : The one-dimensional FFT, with definitions and conventions used.
rfftn : The *n*-dimensional FFT of real input.
fft2 : The two-dimensional 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.

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))
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]]])
>>> np.fft.fftn(a, (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
>>> [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))
<matplotlib.image.AxesImage object at 0x...>
>>> plt.show()

Vous êtes un professionnel et vous avez besoin d'une formation ? Programmation Python
Les fondamentaux Voir le programme détaillé