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# scipy.fft.fftn

scipy.fft.fftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *, plan=None)

  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 `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 `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.

      New in version 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()