scipy.fft.

ihfft#

scipy.fft.ihfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *, plan=None)[source]#

Compute the inverse FFT of a signal that has Hermitian symmetry.

Parameters:

xarray_like: Input array.
nint, optional: Length of the inverse FFT, the number of points along transformation axis in the input to use. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.
axisint, optional: Axis over which to compute the inverse FFT. If not given, the last axis is used.
norm{“backward”, “ortho”, “forward”}, optional: Normalization mode (see fft). Default is “backward”.
overwrite_xbool, optional: If True, the contents of x can be destroyed; the default is False. See fft for more details.
workersint, 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.
planobject, optional: This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.

Added in version 1.5.0.

Returns:

outcomplex 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//2 + 1.

See also

hfft, irfft

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

ihfft 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 Support for the array API standard for more information.

Examples

>>> from scipy.fft import ifft, ihfft
>>> import numpy as np
>>> spectrum = np.array([ 15, -4, 0, -1, 0, -4])
>>> ifft(spectrum)
array([1.+0.j,  2.+0.j,  3.+0.j,  4.+0.j,  3.+0.j,  2.+0.j]) # may vary
>>> ihfft(spectrum)
array([ 1.-0.j,  2.-0.j,  3.-0.j,  4.-0.j]) # may vary