MULTIRESOLUTION ANALYSIS OF A CLASS OF NONSTATIONARY PROCESSES

Processing nonstationary signals is an important and challenging probl em. We focus on the class of nonstationary processes with stationary i ncrements of an arbitrary order, and place them in a multiscale framew ork. Unlike other related studies, we concentrate on the discrete-time analysis and derive a number of new results in addition to placing th e related existing ones in the same framework. We extend the study to various parametric models for which we derive the resulting multiresol ution description. We show that wide-sense stationarity may be achieve d by adequately selecting the analysis wavelet. After generalizing the study to wavelet packet analysis, we show that the latter possesses a dditional properties which are useful in the presence of other types o f nonstationarities.