Adaptive wave field synthesis with independent radiation mode control for active sound field reproduction: Theory

Abstract

Sound field reproduction finds applications in music or audio reproduction and experimental acoustics. For audio applications, sound field reproduction can be used to artificially reproduce the spatial character of natural hearing. The general objective is then to reproduce a sound field in a real reproduction environment. Wave field synthesis (WFS) is a known open-loop technology which assumes that the reproduction environment is anechoic. For classical WFS, the room response thus reduces the quality of the physical sound field reproduction. In this paper, adaptive wave field synthesis (AWFS) is analytically investigated as an adaptive sound field reproduction system combining WFS and active control with a limited number of reproduction error sensors to compensate the response of the listening environment. The primary point of this paper is the definition of AWFS. Therefore, the fundamental behavior of AWFS is illustrated by analytical considerations and simple free-field simulation results. As demonstrated, AWFS is fundamentally related to WFS and “Ambisonics.” The paper introduces independent adaptive control of sound field reproduction on the basis of radiation modes, via the singular value decomposition of the transfer impedance matrix. Possible practical independent control of radiation modes for AWFS is discussed.