A Digital Signal Processing Method for Actual Stochastic System with Discrete Level of a Mixed Model Type and Its Application to the Reverberation Time Estimation Problem in a Room Acoustic Environment

Abstract

In this paper, a state estimation algorithm especially matched to the computer technique with successive observations for the actual complicated stochastic system is derived. First, in the actual situation when the stochastic system is affected by a multiplicative random factor as well as an additive noise factor of arbitrary probability distribution form, a mixed type stochastic process model is established. Next, by considering the level quantized mechanism of the actual observation, a recursive algorithm of digital filter to estimate the momentary unknown state is theoretically proposed in an expansion form of the well-known Bayes' theorem. Finally, the effectiveness of the proposed theory is experimentally confirmed by applying it to the environmental noise data in the room acoustics.