xrscipy.fft.hfft

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

Compute the FFT of a signal that has Hermitian symmetry, i.e., a real

spectrum.

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 - 2, where m is the length of the transformed axis of the input. To get an odd number of output points, n must be specified, for instance, as 2*m - 1 in the typical case,

Return type:

ndarray

Raises:

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

See also

rfft

Compute the 1-D FFT for real input.

ihfft

The inverse of hfft.

hfftn

Compute the N-D FFT of a Hermitian signal.

scipy.fft.hfft

scipy.fft.hfft : Original scipy implementation

Notes

hfft/ihfft are a pair analogous to rfft/irfft, but for the opposite case: here the signal has Hermitian symmetry in the time domain and is real in the frequency domain. So, here, it’s hfft, for which you must supply the length of the result if it is to be odd. * even: ihfft(hfft(a, 2*len(a) - 2) == a, within roundoff error, * odd: ihfft(hfft(a, 2*len(a) - 1) == a, within roundoff error.

Examples

>>> from scipy.fft import fft, hfft
>>> import numpy as np
>>> a = 2 * np.pi * np.arange(10) / 10
>>> signal = np.cos(a) + 3j * np.sin(3 * a)
>>> fft(signal).round(10)
array([ -0.+0.j,   5.+0.j,  -0.+0.j,  15.-0.j,   0.+0.j,   0.+0.j,
        -0.+0.j, -15.-0.j,   0.+0.j,   5.+0.j])

Examples

>>> hfft(signal[:6]).round(10) # Input first half of signal
array([  0.,   5.,   0.,  15.,  -0.,   0.,   0., -15.,  -0.,   5.])

Examples

>>> hfft(signal, 10)  # Input entire signal and truncate
array([  0.,   5.,   0.,  15.,  -0.,   0.,   0., -15.,  -0.,   5.])