Module hfft 

Hermitian Fast Fourier Transform (HFFT) module

This module provides functions for computing the Hermitian Fast Fourier Transform (HFFT) and its inverse (IHFFT). These functions handle complex-valued signals with real spectra.

Implementation Notes

The HFFT functions are particularly sensitive to numerical precision issues due to their reliance on Hermitian symmetry properties. When using these functions:

1. Normalization: Pay close attention to the normalization parameter, as it significantly affects scaling in round-trip transformations.

2. Precision: Hermitian symmetry requires that the imaginary part of certain components be exactly zero, which may not be possible due to floating-point precision. The functions apply reasonable tolerances to handle these cases.

3. Round-Trip Transformations: When performing hfft followed by ihfft (or vice versa), you may need to apply scaling factors to recover the original signal amplitudes accurately.

4. Multi-dimensional Transforms: 2D and N-dimensional transforms have additional complexity regarding Hermitian symmetry across multiple dimensions. Care should be taken when working with these functions.

Functions

create_hermitian_symmetric_signal

Create a Hermitian-symmetric array from a real-valued amplitude spectrum.

enforce_hermitian_symmetry

Enforce Hermitian symmetry on a 2D complex array.

enforce_hermitian_symmetry_nd

Enforce Hermitian symmetry on an N-dimensional complex array.

hfft

Compute the 1-dimensional discrete Fourier Transform for a Hermitian-symmetric input.

hfft2

Compute the 2-dimensional discrete Fourier Transform for a Hermitian-symmetric input.

hfftn

Compute the N-dimensional discrete Fourier Transform for Hermitian-symmetric input.

ihfft

Compute the 1-dimensional inverse Hermitian FFT.

ihfft2

Compute the 2-dimensional inverse Hermitian FFT.

ihfftn

Compute the N-dimensional inverse Hermitian FFT.

is_hermitian_symmetric

Check if an array is approximately Hermitian-symmetric.