Advanced Processing of Nonuniformly Sampled Non-Stationary Signals

A signal is stationary if its statistical characteristics do not change with time. Signals of practical interest often do not comply with this requirement [1]. It has been quit difficult to satisfactorily handle non-stationary signals using conceptualizations based on stationarity, as it is assumed, for example, by classical Fourier transform. Nonstationary signals justify the need for joint time-frequency analysis and representation. Non-stationary signals may be divided into two types: momentarily transient and persistent. The momentarily transient signal has a brief, finite duration. The persistent non-stationary signal has continuous time-varying behavior. In practice the time-frequency representation is characterized by points on a time-frequency gram with a finite duration time axis and finite bandwidth frequency axis. Time-frequency analysis typically deals with signals for which the instantaneous frequency bandwidth is considerably narrower than the whole bandwidth of signal spectral characteristics [2]. As examples can be quoted chirps, Doppler signals, frequency tracking etc. To process signals digitally they should be sampled. The Nyquist criterion gives us a theoretical limit to what rate we have to periodically sample a signal that contains data at a certain maximum frequency. Once we sample below the Nyquist rate we get the spectral analysis results, which have corrupting artifacts – so called “aliases”. A dilemma concerning the choice of sampling rate arises: on the one hand the maximum signal frequency defines sampling frequency according to Nyquist, while on the other hand the narrow instantaneous bandwidth of signal at each time moment allows a considerably lower sampling density. One possible course of action in such a case is to use a nonuniform sampling technique. The proper application of nonuniform sampling suppresses the frequency aliasing and allows the use of a sampling density below the Nyquist rate [3]. It should be stated that nonuniformly taken signal samples require the focusing of more attention on the signal processing algorithm. The benefit achieved by suppression of frequency aliasing could translate into some other corrupting artifact, for example, the increased noise floor of spectrogram as it is usually for the standard spectral estimation algorithms. In this paper the advanced signal processing method will be discussed, which will provide high frequency and time resolution in a wide dynamic range of analysis. Typical Time-frequency representations