erformed 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()

rK