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

fftn.__doc__

    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 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
    >>> 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()