Recent Applications of Number-Theoretic Sequences in Audio and Acoustics

Abstract

Manfred R. Schroeder made influential contributions to acoustics by applying number theory. He introduced number-theory sequences in room impulse response measurements, applied number-theoretical sequences to shape wall surfaces for diffuse sound reflections. Another area Manfred Schroeder made broad impact is invention of an artificial reverberator using all-pass transfer- function properties to create colorless reverberation using a simple algorithm. Vast research activities and engineering developments over past decades have extended Schroeder’s work involving artificial reverberators, artificial stereo and applications of maximum-length sequences. This chapter briefs a number of recent applications of maximum-length and quadratic-residue sequences, such as simultaneous dual/multiple sources measurements in acoustical tomography, in artificial pseudo-binaural reverberation, in decorrelation for spatial audio signals, and room acoustic diffuser design.