Measure of complexity of wave motions and crosscorrelation coefficient in reverberant fields.

Abstract

In this paper, the complexity of wave motions has been formulated in order to more detailedly than previously consider the complexities of reverberant sound fields, and the difference of complexity between two separate points has been described in an attempt to find a measure of diffuseness in these fields. The reverberant fields are assumed to be sound fields where random plane waves propagate two- or three-dimensionally. Entropy H (=h2-h1)and energy-entropy product K are used to define the complexity of wave motions, where h1, h2 are entropies by sound pressures p1, p2, respectively. Then H is compared with the cross-correlation coefficient R calculated from same sound pressures. Furthermore, K is obtained by considering energy dissipation with propagation, and its properties are discussed as well as those of H. The results show that the entropy of sinusoidal wave is in a complementary relationship with the cross-correlation coefficient; H=1-R, and that it may be convenient to measure since the cross-correlation coefficient is inseparable into two entropies. Either the entropy or the energy-entropy product is also found to be required at audio frequencies as a measure of the complexity of wave motions (i.e. approximately K=A0H, A0=const. for this case). Because of the lack of a quantity giving degrees of directional distribution, our introduced measure is as yet insufficient to accurately measure the diffuseness of sound fields, but it may be fairly near to the corrected measure.