A Fourier series based Data compression model for Acoustic transfer function

Abstract

This paper addresses a modeling of acoustic transfer function using Fourier series expansion. A transfer function set consisting of many transfer functions, which are obtained by measurements or geometrical calculations, is usually required for applications like sound source localization and separation. The data size of the set is often so large because of the fine resolution. Such a large set is unsuitable for embedded systems, e.g. robots and mobile phones due to the limitation of their storage size and computational resources. To avoid this problem, a novel modeling of acoustic transfer function is proposed, which reduces the size of the transfer function set smaller enough for embedded systems by means of function representation based on Fourier series. Since the proposed modeling is based on the function representation, the interpolation between two adjacent measured transfer functions is naturally obtained. This allows the fine resolution in sound source localization and separation compared to the application that any conventional transfer function sets are used. The error of the proposed model was about 2 dB in amplitude and 15° in phase on average in the numerical simulation. The proposed model is also evaluated in sound source localization. The experimental results indicated that the localization error was 3.5° even though the memory usage and the calculation time decreased 97% and 24% respectively, when the conventional model results was 100%.