Time-varying filter modelling and time-frequency characterisation of non-stationary sound fields due to a moving source
This thesis deals with the problems of modelling, interpretation and estimation of `non-stationary' processes with particular reference to acoustic problems. A common assumption in the modelling 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. In the thesis two methods are studied for the characterisation of such non-stationary processes; i) `time-frequency' spectral characterisation and ii) time-varying filter modelling. Two major candidates for `time-frequency' (time-varying) spectral characterisation of non-stationary processes are the Wigner-Ville spectrum and Priestley's evolutionary spectrum. Properties, prediction and estimation of the two time-frequency spectra and the relation 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 modelling 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 has only been 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 (i) the source acoustic directionality pattern and (ii) time-varying delay estimation problems, are formulated and solved in terms of the covariance-equivalent models, and simulation studies are also performed. The simulation results justify that the covariance-equivalent method is an effective characterisation of such non-stationary processes.