Abstract In the situation of evaluating an environmental sound phenomenon, there is often the necessity of estimating statistical quantities such as the mean, variance and the other higher order moments, owing to the arbitrariness of the phenomena and the complexity of human response to them. Furthermore, the measured data is usually contaminated by background noise of an arbitrary distribution type. In this paper, a unified methodology for detecting the unknown sound state in the presence of such background noise is proposed. An hierarchical expansion expression for the probability density function is developed, based on a successive differential procedure. This digital filter in a wide sense corresponds exactly with the well-known Kalman filter in the ideal case when the stochastic sound system is linear and Gaussian. The validity of the proposed wide sense digital filter has been experimentally confirmed by several applications to observed data. Three cases are presented, namely: (i) estimating the unknown reverberation time of a room; (ii) estimating the parameters of a sound insulation system between two reverberant rooms; (iii) estimating the waveform of traffic noise strongly contaminated by background noise.
[1]
M. S. Bartlett,et al.
An introduction to stochastic processes, with special reference to methods and applications
,
1955
.
[2]
R. E. Kalman,et al.
A New Approach to Linear Filtering and Prediction Problems
,
2002
.
[3]
Mitsuo Ohta,et al.
General statistical treatment of the response of a nonlinear rectifying device to a stationary random input (Corresp.)
,
1968,
IEEE Trans. Inf. Theory.
[4]
W. Root,et al.
An introduction to the theory of random signals and noise
,
1958
.
[5]
Malcolm J. Crocker,et al.
Sound transmission using statistical energy analysis
,
1969
.
[6]
R. H. Battin,et al.
Random Processes in Automatic Control.
,
1957
.