flopscope.

flopscope.numpy.fft.ifft2

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

Compute the 2-dimensional inverse discrete Fourier Transform.

Adapted from NumPy docs np.fft.ifft2

Areafft
Typecustom
NumPy Refnp.fft.ifft2
Cost
5N⋅⌈log⁡2N⌉5N \cdot \lceil\log_2 N\rceil
Flopscope Context

Inverse 2-D complex FFT. Cost: 5*N*ceil(log2(N)), N=prod(s) (Cooley-Tukey radix-2; Van Loan 1992 §1.4).

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 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 2.0.
Deprecated since 2.0.
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 2.0.
norm:{"backward", "ortho", "forward"}, optional

Normalization mode (see flops.fft). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.

Added in version 1.20.0.
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).

Added 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

  • flops.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 flops.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 flopscope.numpy as fnp
>>> a = 4 * flops.eye(4)
>>> flops.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]])