Asynchronous Representation and Processing of Non–stationary Signals in a Time-frequency Context

Non–stationarity relates to the variation over time of the statistics of a signal. Therefore, signals from practical applications which are realizations of non–stationary processes are difficult to represent and to process. In this paper, we provide a comprehensive discussion of the asynchronous representation and processing of non–stationary signals using a time-frequency framework. Power consumption and type of processing imposed by the size of the devices in many applications motivate the use of asynchronous, rather than conventional synchronous, approaches. This leads to the consideration of non–uniform, signal–dependent level–crossing and asynchronous sigma delta modulator (ASDM) based sampling. Reconstruction from a non– uniform sampled signal is made possible by connecting the sinc and the Prolate Spheroidal Wave (PSW) functions — a more appropriate basis. Two decomposition procedures are considered. One is based on the ASDM that generalizes the Haar wavelet representation and is used for representing analog non–stationary signals. The second decomposer is for representing discrete non– stationary signals. It is based on a linear-chirp based transform that provides local time-frequency parametric representations based on linear chirps as intrinsic mode functions. Important applications of these procedures are the compression and processing of biomedical signals as it will be illustrated.