This repository numerically validates and gives examples on how to apply the symmetries of complex-valued spherical harmonic (SH) and circular harmonic (CH) expansions given in
Thomas Deppisch and Jens Ahrens,
"Symmetries in Complex-Valued Spherical Harmonic Processing of Real-Valued Signals,"
Proc. of the Annual German Conference on Acoustics (DAGA), 2025.
Considering these symmetries in signal processing algorithms that involve complex-valued SHs (or CHs) and are based on real-valued (time-domain) signals may significantly reduce the required computations and memory.
The validation scripts use SH implementations from the Spherical Harmonic Transform Library, which is linked as submodule under dependencies.
Clone this repository using git clone --recurse-submodules to make sure the corresponding functions are available.