scipy.fft.ifft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *, plan=None)[source]#

Compute the 2-D inverse discrete Fourier Transform.

This function computes the inverse of the 2-D discrete Fourier Transform over any number of axes in an M-D array by means of the Fast Fourier Transform (FFT). In other words, ifft2(fft2(x)) == x 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.


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. 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.

axessequence 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_xbool, optional

If True, the contents of x can be destroyed; the default is False. See fft for more details.

workersint, 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.

planobject, optional

This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.

Added in version 1.5.0.

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.


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


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

See also


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


The inverse of the N-D FFT.


The 1-D FFT.


The 1-D inverse FFT.


ifft2 is just ifftn with a different default for axes.

See ifftn for details and a plotting example, and 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.


>>> import scipy.fft
>>> import numpy as np
>>> x = 4 * np.eye(4)
>>> scipy.fft.ifft2(x)
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]])