numpy.fft.hfft(a, n=None, axis=-1, norm=None)
[source]
Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum.
Parameters: |
a : array_like The input array. n : int, optional Length of the transformed axis of the output. For axis : int, optional Axis over which to compute the FFT. If not given, the last axis is used. norm : {None, “ortho”}, optional Normalization mode (see New in version 1.10.0. |
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Returns: |
out : ndarray The truncated or zero-padded input, transformed along the axis indicated by |
Raises: |
IndexError If |
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.
ihfft(hfft(a, 2*len(a) - 2) == a
, within roundoff error,ihfft(hfft(a, 2*len(a) - 1) == a
, within roundoff error.>>> signal = np.array([1, 2, 3, 4, 3, 2]) >>> np.fft.fft(signal) array([ 15.+0.j, -4.+0.j, 0.+0.j, -1.-0.j, 0.+0.j, -4.+0.j]) >>> np.fft.hfft(signal[:4]) # Input first half of signal array([ 15., -4., 0., -1., 0., -4.]) >>> np.fft.hfft(signal, 6) # Input entire signal and truncate array([ 15., -4., 0., -1., 0., -4.])
>>> signal = np.array([[1, 1.j], [-1.j, 2]]) >>> np.conj(signal.T) - signal # check Hermitian symmetry array([[ 0.-0.j, 0.+0.j], [ 0.+0.j, 0.-0.j]]) >>> freq_spectrum = np.fft.hfft(signal) >>> freq_spectrum array([[ 1., 1.], [ 2., -2.]])
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https://docs.scipy.org/doc/numpy-1.14.2/reference/generated/numpy.fft.hfft.html