numpy.fft.hfft¶

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
 aarray_like
The input array.
 nint, 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 be2*(m1)
wherem
is the length of the input along the axis specified by axis. axisint, optional
Axis over which to compute the FFT. If not given, the last axis is used.
 norm{“backward”, “ortho”, “forward”}, optional
New in version 1.10.0.
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.New in version 1.20.0: The “backward”, “forward” values were added.
 Returns
 outndarray
The truncated or zeropadded 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
wherem
is the length of the transformed axis of the input. To get an odd number of output points, n must be specified, for instance as2*m  1
in the typical case,
 Raises
 IndexError
If axis is larger than the last axis of a.
Notes
hfft
/ihfft
are a pair analogous torfft
/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’shfft
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.Examples
>>> 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.]])