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# numpy.fft.ifft2

fft.ifft2(a, s=None, axes=(-2, -1), norm=None, out=None)

  Compute the 2-dimensional inverse discrete Fourier Transform.

  This function computes the inverse of the 2-dimensional discrete Fourier Transform over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). In other words, `ifft2(fft2(a)) == a` to within numerical accuracy. By default, the inverse transform is computed over the last two axes of the input array.

  The input, analogously to `ifft`, should be ordered in the same way as is returned by `fft2`, i.e. it should have the term for zero frequency in the low-order corner of the two 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 both axes, in order of decreasingly negative frequency.

  Parameters:
    a array_like

      Input array, can be complex.

    s sequence of ints, optional

      Shape (length of each axis) of the output (`s[0]` refers to axis 0, `s[1]` to axis 1, etc.). This corresponds to n for `ifft(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.

      Changed in version 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. See notes for issue on `ifft` zero padding.

      Deprecated since version 2.0: If s is not `None`, axes must not be `None` either.

      Deprecated since version 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 two axes are used. A repeated index in axes means the transform over that axis is performed multiple times. A one-element sequence means that a one-dimensional FFT is performed. Default: `(-2, -1)`.

      Deprecated since version 2.0: If s is specified, the corresponding axes to be transformed must not be `None`.

    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.

      New in version 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`).

      New in version 2.0.0.

  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 than the number of axes of a.

  See also

  `numpy.fft`

    Overall view of discrete Fourier transforms, with definitions and conventions used.

  `fft2`

    The forward 2-dimensional FFT, of which `ifft2` is the inverse.

  `ifftn`

    The inverse of the n-dimensional FFT.

  `fft`

    The one-dimensional FFT.

  `ifft`

    The one-dimensional inverse FFT.

  Notes

  `ifft2` is just `ifftn` with a different default for axes.

  See `ifftn` for details and a plotting example, and `numpy.fft` for definition and conventions used.

  Zero-padding, analogously with `ifft`, is performed by appending zeros to the input along the specified dimension. Although this is the common approach, it might lead to surprising results. If another form of zero padding is desired, it must be performed before `ifft2` is called.

  Examples

      >>> import numpy as np
      >>> a = 4 * np.eye(4)
      >>> np.fft.ifft2(a)
      array([[1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j], # may vary
             [0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],
             [0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
             [0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]])