nlcpy.fft.hfft
- nlcpy.fft.hfft(a, n=None, axis=- 1, norm=None)[ソース]
Computes 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*(m-1)
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. If axis is larger than the last axis of a, IndexError occurs.
- norm{None, "ortho"},optional
Normalization mode. By default(None), the transforms are unscaled. It norm is set to "ortho", the return values will be scaled by .
- Returns
- outndarray
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 as2*m - 1
in the typical case,
参考
注釈
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
>>> import nlcpy as vp >>> signal = vp.array([1, 2, 3, 4, 3, 2]) >>> vp.fft.fft(signal) array([15.+0.j, -4.+0.j, 0.+0.j, -1.+0.j, 0.+0.j, -4.+0.j]) # may vary >>> vp.fft.hfft(signal[:4]) # Input first half of signal array([15., -4., 0., -1., 0., -4.]) >>> vp.fft.hfft(signal, 6) # Input entire signal and truncate array([15., -4., 0., -1., 0., -4.])
>>> signal = vp.array([[1, 1.j], [-1.j, 2]]) >>> vp.conj(signal.T) - signal # check Hermitian symmetry array([[ 0.-0.j, -0.+0.j], [ 0.+0.j, 0.-0.j]]) >>> freq_spectrum = vp.fft.hfft(signal) >>> freq_spectrum array([[ 1., 1.], [ 2., -2.]])