Evolutionary Spectrum and Bispectrum Estimation of a Nonstationary Process

The modeling of a non-stationary process is a problem of great interest and has many applications in diverse fields in signal processing. In this paper, an algorithm for estimating the shiftvariant (SV) parameters of a non-stationary process, using orthogonal projection, is proposed. These parameters can be used for estimating the evolutionary spectrum (ES), a time-frequency distribution, of a non-stationary process. The ES is then estimated with an order based on the dimensionality of the expanding orthogonal polynomials (OPs). In the proposed method the process is decomposed to its basic elements by projecting it, recursively, onto elementary OPs. Simulations are presented when the process has either single or multiple SV parameters. We have also shown that if the output of the SV system is corrupted by stationary/nonstationary noise with symmetric distribution, the noise can be removed using the evolutionary bispectrum (EB), and simulation is given to show the powerful of the EB.