Spatial Filter Bank in the Spherical Harmonic Domain: Reconstruction and Application

Filter banks are an integral part of modern signal processing. They may also be applied to spatial filtering and the employed spatial filters can be designed with a specific shape for the analysis, e. g. suppressing side-lobes. After extracting spatially constrained signals from spherical harmonic (SH) input, i. e. filter bank analysis, many applications demand for a re-synthesis of the associated sector signals to the SH domain. This paper hence derives the complementary spatial filter bank reconstruction. The criterion for perfect reconstruction, and energy preserving reconstruction are given and implemented into the design. The filter bank is formulated such that for axisymmetric patterns both criteria can be met by only minor modification to the reconstruction stage. Its application is then demonstrated for both scenarios, perfect reconstruction and energy preservation of SH input signals.