xrscipy.fft.ifftn

xrscipy.fft.ifftn(x, coord, n=None, norm=None)

Compute the N-D inverse discrete Fourier Transform.

This function computes the inverse of the N-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, ifftn(fftn(x)) == x to within numerical accuracy.

The input, analogously to ifft, should be ordered in the same way as is returned by fftn, i.e., it should have the term for zero frequency in all axes in the low-order corner, the positive frequency terms in the first half of all axes, the term for the Nyquist frequency in the middle of all axes and the negative frequency terms in the second half of all axes, in order of decreasingly negative frequency.

Parameters:

  • x (xarray object) – The data to transform.

  • s (mapping from coords to size, optional) – the shape of the result.

  • axes (sequence of ints, optional) – Axes over which to compute the IFFT. If not given, the last len(s) axes are used, or all axes if s is also not specified.

  • norm ({"backward", "ortho", "forward"}, optional) – Normalization mode (see fft). Default is “backward”.

Returns:

out – The truncated or zero-padded input, transformed along the axes indicated by axes, or by a combination of s or x, as explained in the parameters section above.

Return type:

complex ndarray

Raises:

  • ValueError – If s and axes have different length.

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

See also

fftn

The forward N-D FFT, of which ifftn is the inverse.

ifft

The 1-D inverse FFT.

ifft2

The 2-D inverse FFT.

ifftshift

Undoes fftshift, shifts zero-frequency terms to beginning of array.

scipy.fft.ifftn

scipy.fft.ifftn : Original scipy implementation

Notes

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 ifftn is called.

Examples

>>> import scipy.fft
>>> import numpy as np
>>> x = np.eye(4)
>>> scipy.fft.ifftn(scipy.fft.fftn(x, axes=(0,)), axes=(1,))
array([[1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j], # may vary
       [0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],
       [0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
       [0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j]])

Create and plot an image with band-limited frequency content:

Examples

>>> import matplotlib.pyplot as plt
>>> rng = np.random.default_rng()
>>> n = np.zeros((200,200), dtype=complex)
>>> n[60:80, 20:40] = np.exp(1j*rng.uniform(0, 2*np.pi, (20, 20)))
>>> im = scipy.fft.ifftn(n).real
>>> plt.imshow(im)
<matplotlib.image.AxesImage object at 0x...>

Examples

>>> plt.show()