Symmetries in Complex-Valued Spherical Harmonic Processing of Real-Valued Signals
Paper i proceeding, 2025

Spherical harmonics (SHs) are widely used in audio and acoustics to represent sound fields and their spatial information. While SH expansions of real-valued functions can equivalently employ real- or complex-valued definitions of SH basis functions, real-valued definitions reduce computational load and storage needs. Researchers, however, often prefer a complex definition for its concise handling of operations like rotations and translations, which comes at the expense of partially redundant computations in practical implementations. To mitigate this downside, this work examines symmetries in expansions of real signals in terms of complex SHs in both the time and frequency domain and identifies redundancies akin to Hermitian symmetry in Fourier transforms. The resulting collection of the symmetry properties of SHs and circular harmonics (CHs) can be leveraged to limit computations to the non-redundant coefficients, significantly reducing the computational complexity and storage requirements in algorithms using complex-valued SHs.

acoustics

microphone array

signal processing

Room impulse response

Författare

Thomas Deppisch

Chalmers, Arkitektur och samhällsbyggnadsteknik, Teknisk akustik

Jens Ahrens

Chalmers, Arkitektur och samhällsbyggnadsteknik, Teknisk akustik

Proceedings "Fortschritte der Akustik - DAGA 2024"

Vol. In press

DAS/DAGA Annual German Conference on Acoustics
Copenhagen, Denmark,

Styrkeområden

Informations- och kommunikationsteknik

Ämneskategorier (SSIF 2025)

Signalbehandling

Mer information

Senast uppdaterat

2025-04-04