xrscipy.fft.irfft

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

Computes the inverse of rfft.

This function computes the inverse of the 1-D n-point discrete Fourier Transform of real input computed by rfft. In other words, irfft(rfft(x), len(x)) == x to within numerical accuracy. (See Notes below for why len(a) is necessary here.)

The input is expected to be in the form returned by rfft, i.e., the real zero-frequency term followed by the complex positive frequency terms in order of increasing frequency. Since the discrete Fourier Transform of real input is Hermitian-symmetric, the negative frequency terms are taken to be the complex conjugates of the corresponding positive frequency terms.

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

  • coord (string) – The axis along which the transform is applied. The coordinate must be evenly spaced.

  • n (int, optional) – Length of the transformed axis of the output. For n output points, n//2+1 input points are necessary. If the input is longer than this, it is cropped. If it is shorter than this, it is padded with zeros. If n is not given, it is taken to be 2*(m-1), where m is the length of the input along the axis specified by axis.

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

Returns:

out – The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified. The length of the transformed axis is n, or, if n is not given, 2*(m-1) where m is the length of the transformed axis of the input. To get an odd number of output points, n must be specified.

Return type:

ndarray

Raises:

IndexError – If axis is larger than the last axis of x.

See also

rfft

The 1-D FFT of real input, of which irfft is inverse.

fft

The 1-D FFT.

irfft2

The inverse of the 2-D FFT of real input.

irfftn

The inverse of the N-D FFT of real input.

scipy.fft.irfft

scipy.fft.irfft : Original scipy implementation

Notes

Returns the real valued n-point inverse discrete Fourier transform of x, where x contains the non-negative frequency terms of a Hermitian-symmetric sequence. n is the length of the result, not the input.

If you specify an n such that a must be zero-padded or truncated, the extra/removed values will be added/removed at high frequencies. One can thus resample a series to m points via Fourier interpolation by: a_resamp = irfft(rfft(a), m).

The default value of n assumes an even output length. By the Hermitian symmetry, the last imaginary component must be 0 and so is ignored. To avoid losing information, the correct length of the real input must be given.

Examples

>>> import scipy.fft
>>> scipy.fft.ifft([1, -1j, -1, 1j])
array([0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]) # may vary

Examples

>>> scipy.fft.irfft([1, -1j, -1])
array([0.,  1.,  0.,  0.])

Notice how the last term in the input to the ordinary ifft is the complex conjugate of the second term, and the output has zero imaginary part everywhere. When calling irfft, the negative frequencies are not specified, and the output array is purely real.