hfft(a, n=None, axis=-1, norm=None)¶
Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum.
The input array.
Length of the transformed axis of the output. For n output
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
m is the length of the input along the axis specified by
Axis over which to compute the FFT. If not given, the last axis is used.
Normalization mode (see
numpy.fft). Default is None.
New in version 1.10.0.
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,
If axis is larger than the last axis of a.
ihfft are a pair analogous to
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
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.
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,
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.
>>> 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) >>> freq_spectrum array([[ 1., 1.], [ 2., -2.]])