bundles / numpy 2.4.4 / numpy / fft / hfft
_ArrayFunctionDispatcher
numpy.fft:hfft
source: /numpy/fft/_pocketfft.py :529
Signature
def hfft ( a , n = None , axis = -1 , norm = None , out = None ) Summary
Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum.
Parameters
a: array_likeThe input array.
n: int, optionalLength of the transformed axis of the output. For
noutput points,n//2 + 1input points are necessary. If the input is longer than this, it is cropped. If it is shorter than this, it is padded with zeros. Ifnis not given, it is taken to be2*(m-1)wheremis the length of the input along the axis specified byaxis.axis: int, optionalAxis over which to compute the FFT. If not given, the last axis is used.
norm: {"backward", "ortho", "forward"}, optionalNormalization mode (see numpy.fft). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.
out: ndarray, optionalIf provided, the result will be placed in this array. It should be of the appropriate shape and dtype.
Returns
out: ndarrayThe truncated or zero-padded input, transformed along the axis indicated by
axis, or the last one ifaxisis not specified. The length of the transformed axis isn, or, ifnis not given,2*m - 2wheremis the length of the transformed axis of the input. To get an odd number of output points,nmust be specified, for instance as2*m - 1in the typical case,
Raises
: IndexErrorIf
axisis not a valid axis ofa.
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.
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 numpy as np signal = np.array([1, 2, 3, 4, 3, 2])✓
np.fft.fft(signal) np.fft.hfft(signal[:4]) # Input first half of signal np.fft.hfft(signal, 6) # Input entire signal and truncate✗
signal = np.array([[1, 1.j], [-1.j, 2]])
✓np.conj(signal.T) - signal # check Hermitian symmetry
✗freq_spectrum = np.fft.hfft(signal) freq_spectrum✓
See also
Aliases
-
numpy.fft.hfft