numpy.fft.hfft¶
- 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 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 determined from the length of the input along the axis specified by axis.
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 numpy.fft). Default is None.
New in version 1.10.0.
Returns: out : ndarray
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,
Raises: IndexError
If axis is larger than the last axis of a.
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
>>> 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.]])