Parametric estimation of time-varying components using orthogonal bases

For nonstationary processes, classical frequency estimation methods are incapable of describing and showing the information embedded in the process. That is, because the statistical characteristics (SC) of the nonstationary processes are changing with time, estimation methods based on the stationarity assumption do not reflect this variation. Therefore, the idea of the time-frequency (TF) distribution has been introduced in the literature. Different methods for estimating the TF distribution (TFD) of a nonstationary process have also been proposed in the literature. All of these methods, however, depend on the degree of nonstationarity (DON) of the process, which, although of utmost importance, has not been yet addressed in the literature. In this paper, an algorithm for estimating the time-varying components (TVCs), and hence the TF kernel, of a non-stationary process by using orthogonal projection is proposed. The process is carried out by projecting each component of the process onto an expanding orthogonal basis. The TF kernel is then estimated with an order based on the dimensionality of the expanding orthogonal basis. Some experimental results are presented when the process has either single or multiple TVCs. This revised version was published online in June 2006 with corrections to the Cover Date.