hfft(a, n=None, axis=-1, norm=None)
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.
The correct interpretation of the hermitian input depends on the length of the original data, as given by n. This is because each input shape could correspond to either an odd or even length signal. By default, hfft
assumes an even output length which puts the last entry at the Nyquist frequency; aliasing with its symmetric counterpart. By Hermitian symmetry, the value is thus treated as purely real. To avoid losing information, the shape of the full signal must be given.
The input array.
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 :None:None:`axis`.
Axis over which to compute the FFT. If not given, the last axis is used.
Normalization mode (see numpy.fft
). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.
The "backward", "forward" values were added.
If :None:None:`axis` is not a valid axis of a.
The truncated or zero-padded input, transformed along the axis indicated by :None:None:`axis`, or the last one if :None:None:`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,
Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum.
ihfft
The inverse of :None:None:`hfft`.
rfft
Compute the one-dimensional FFT for real input.
>>> 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]) # may vary
>>> 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], # may vary [ 0.+0.j, 0.-0.j]])
>>> freq_spectrum = np.fft.hfft(signal)See :
... freq_spectrum array([[ 1., 1.], [ 2., -2.]])
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.fft.hfft
numpy.fft.ihfft
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