Time-varying parameter estimation of a non-stationary signal using orthonormal bases

For non-stationary signals, classical frequency estimation methods are incapable of describing and showing the information embedded in the signal. That is, because the characteristics of the non-stationary signals are changing with time, estimation methods based on the stationarity assumption do not rifled this variation. Different methods for estimating the time-frequency distribution (TFD) of a non-stationary signal have been proposed in references [3], [11] and [12] and the references therein, however, all of these methods depend on the degree of the non-stationarity of the process, which, although of its utmost importance, has not been yet addressed in the literature. In this paper, an algorithm for estimating the time-varying components, and hence the time-frequency (TF) kernel, of a non-stationary signal by using orthogonal projection is presented. The process is done by projecting each component of the signal onto an expanding orthogonal basis. The TF kernel is then estimated with an order based on the dimensionality of the expanding orthogonal basis.