# scipy.fft.fft2

scipy.fft.fft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *, plan=None)

  Compute the 2-D discrete Fourier Transform

  This function computes the N-D discrete Fourier Transform over any axes in an M-D array by means of the Fast Fourier Transform (FFT). By default, the transform is computed over the last two axes of the input array, i.e., a 2-dimensional 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 each 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 two axes are used.

    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 the last two axes if axes is not given.

  Raises:
    ValueError

      If s and axes have different length, or axes not given and `len(s) != 2`.

    IndexError

      If an element of axes is larger than the number of axes of x.

  See also

  `ifft2`

    The inverse 2-D FFT.

  `fft`

    The 1-D FFT.

  `fftn`

    The N-D FFT.

  `fftshift`

    Shifts zero-frequency terms to the center of the array. For 2-D input, swaps first and third quadrants, and second and fourth quadrants.

  Notes

  `fft2` is just `fftn` with a different default for axes.

  The output, analogously to `fft`, contains the term for zero frequency in the low-order corner of the transformed axes, the positive frequency terms in the first half of these axes, the term for the Nyquist frequency in the middle of the axes and the negative frequency terms in the second half of the axes, in order of decreasingly negative frequency.

  See `fftn` for details and a plotting example, and `fft` for definitions and conventions used.

  Examples

      >>> import scipy.fft
      >>> import numpy as np
      >>> x = np.mgrid[:5, :5][0]
      >>> scipy.fft.fft2(x)
      array([[ 50.  +0.j        ,   0.  +0.j        ,   0.  +0.j        , # may vary
                0.  +0.j        ,   0.  +0.j        ],
             [-12.5+17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
                0.  +0.j        ,   0.  +0.j        ],
             [-12.5 +4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
                0.  +0.j        ,   0.  +0.j        ],
             [-12.5 -4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
                0.  +0.j        ,   0.  +0.j        ],
             [-12.5-17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
                0.  +0.j        ,   0.  +0.j        ]])