Randomness, reflections, and the roots of acoustic impulse responses : applications and effects in spatial audio

Abstract

This thesis is concerned with the analysis of acoustic impulse responses, particularly with a view to understanding and improving applications and algorithms related to virtual auditory environments. The chief contributions of this thesis can be described as follows. An analysis is made of the relation between the roots of random polynomials, known to cluster uniformly about the unit circle, and those of acoustic impulse responses. The roles of both "approximate" onset delay and magnitude decay are explored. This analysis is extended to look at the influence of clusters of roots between sets of acoustic responses upon approximate factorisation algorithms.