nlcpy.fft.ifft2

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

Computes 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. 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. If s and axes have different length, or axes not given and len(s) != 2, ValueError occurs.
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. If an element of axes is larger than than the number of axes of a, IndexError occurs.
norm{None, “ortho”},optional: Normalization mode. By default(None), the transforms are scaled by $1/n$ . It norm is set to “ortho”, the return values will be scaled by $1/\sqrt{n}$ .

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.

See also

fft2: Computes the 2-dimensional discrete fourier transform.
ifftn: Computes the n-dimensional inverse discrete fourier transform.
fft: Computes the one-dimensional discrete fourier transform.
ifft: Computes the one-dimensional inverse discrete fourier transform.

Note

ifft2() is just ifftn() with a different default for axes.

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 nlcpy as vp
>>> a = 4 * vp.eye(4)
>>> vp.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]])