Impact of deleting small magnitude coefficients from spherical harmonic spectrum of sound source directivity

Expressing sound source directivity in the spherical harmonic domain is a popular way of obtaining continuous representation from discrete directivity measurement data and also a potent data compression method. In the latter application, typically the compressing properties of spherical harmonic approximation are evaluated based on the number of coefficients compared to the number of discrete samples of raw measurement data. This paper investigates the possibility of further reducing the amount of data required to store such representation by removing spherical harmonic coefficients of small magnitude. The percentage of reduced coefficients and the reproduction accuracy are determined for different thresholds and analyzed. The results show that over a half of the coefficients can be ignored without a significant impact on the accuracy and further reducing their number leads to relatively small but potentially noticeable deviations in retrieved directivity function. Presented method could lead to more efficient storage of continuous directivity data.

Keywords:

spherical harmonics , sound source directivity , data compression.