Zeros and Room Transfer Functions for Coherent and Incoherent Sound Fields

Distance from a source may be a representative of sound field in a room. The energy ratio of the direct and reverberation would be a possible reference to sound fields, that is a function of the distance, from a macroscopic perspective sound fields. Zeros of room transfer functions are sensitive to the distance from a signal theoretic standard such as magnitude and phase responses. Room transfer functions could be minimum phase in the coherent field close to the sound source. In contrast, transfer functions are non-minimum phase in the incoherent field that is far from the sound source. The zeros distribute following a Cauchy distribution in the complex frequency plane. Transition from the minimum-phase to non-minimum phase transfer functions is rendered by movements of the zeros. The movements may be due to changes in signs of residues for a pair of adjacent poles as the distance farer from the source. Phase responses in the incoherent fields estimated by the number of non-minimum phase zeros could be confirmed by measurements of room impulse responses as well as the density of non-minimum phase zeros. Density of the non-minimum phase zeros could be independent of frequencies.