Statistical Phase Analysis in Rooms

Group delay gives time delay in the envelope. Phase analysis based on a Cauchy distribution of zeros of room transfer functions formulates the group delay due to the reverberation decay as a function of the modal overlap. The group delay shows a limit that is equivalent to TR/13.8 (s) according to the geometric acoustics, as the modal overlap goes high, where TR denotes the reverberation time. Sound fields in rooms could be decomposed into the direct (or coherent) and reverberation (incoherent) fields. The range of the coherent field that is analytically defined following the wave theoretic approach could be estimated by variances in the group delay from propagation phases, too. The variances increase in proportion to square of the sound source distance as expected. Coherent fields (or propagation phases) are mostly governed by minimum-phase zeros, while incoherent fields (or reverberation phases) are dominated by non-minimum phase zeros. A trend of reverberation phases could be linear phase with the group delay of the limit. The variance in phases for coherent field would be a representative of sound fields in rooms by a perspective of statistical phase analysis as well as the reverberation time according to the geometric acoustics.