`scipy.fft._basic:hfft`

source: /scipy/fft/_basic.py :475

Signature

   def     hfft (    x    ,    n    =  None   ,    axis    =  -1   ,    norm    =  None   ,    overwrite_x    =  False   ,    workers    =  None   ,  * ,     plan    =  None     )

Summary

Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum.

Parameters

x : 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 taken to be 2*(m-1), where m is 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 : {"backward", "ortho", "forward"}, optional: Normalization mode (see fft). Default is "backward".
overwrite_x : bool, optional: If True, the contents of x can be destroyed; the default is False. See fft for more details.
workers : int, optional: Maximum number of workers to use for parallel computation. If negative, the value wraps around from os.cpu_count(). See fft for more details.
plan : object, optional: This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
versionadded 1.5.0

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.

Array API Standard Support

hfft has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ✅                   
JAX                   ✅                     ✅                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

from scipy.fft import fft, hfft
import numpy as np
a = 2 * np.pi * np.arange(10) / 10
signal = np.cos(a) + 3j * np.sin(3 * a)
fft(signal).round(10)
hfft(signal[:6]).round(10) # Input first half of signal

✓

hfft(signal, 10)  # Input entire signal and truncate

✗

Aliases

scipy.fft.hfft