numpy.fft.ifft2#

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

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:

aarray_like

Input array, can be complex.

ssequence 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.

axessequence 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.

outcomplex 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:

outcomplex 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]])