Time-varying filter modelling and time-frequency characterisation of nonstationary sound fields due to a moving source

The problems of modeling, interpretation, and estimation of non-stationary processes are examined with particular reference to acoustic problems. A common assumption in the modeling and analysis of a random process is that the process is stationary. Such an assumption may be a satisfactory approximation in many instances, but there are situations in which the processes are obviously non-stationary. In particular, many physical non-stationary processes exhibit a frequency-modulated structure. An important example of such processes is the sound perceived by an observer due to a moving source emitting a random signal. Two methods are studied for the characterization of such non-stationary processes; time frequency spectral characterization and time-varying filter modeling. Two major candidates for time-frequency(time varying) spectral characterization of non-stationary processes are the Wigner-Ville spectrum and Priestly's evolutionary spectrum. Properties, prediction, and estimation of the two time-frequency spectra and the relationship between them are discussed. The time-frequency spectra of the sound field due to a moving source are predicted and these spectra are used as the basis for estimation of the acoustic directionality pattern of the source. As to the time-varying filter modeling of such non-stationary processes, a technique called the covariance-equivalent method is discussed. The covariance-equivalent technique is used to model the sound field due to a moving source emitting a random signal in single-path/single-sensor cases. The covariance-equivalent method, which was only applicable to single-component processes, is extended to include the sound field in multi-path/multi-sensor cases by using the concept of the complex envelope (complex process). Finally, estimation problems of practical importance, including that of the source acoustic directionality pattern and time-varying delay estimation problems, are formulated and solved in terms of the covariance-equivalent models, and simulation studies are also performed.