Statistical Signal Analysis and Processing LABORATORY

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Observing a signal in time is generally insufficient when it comes to the information extraction, hence the need for its frequency content insight. When analysing non-stationary signals, it is necessary to observe the signal energy distribution both over time and frequency simultaneously; a representation commonly referred to as the signal time-frequency distribution (TFD). The energy of the ideal TFD is localised around the instantaneous frequencies (IFs) of the individual components, a feature which is not easily achieved in practice. Indeed, when the observed signal is multicomponent, or when it contains nonlinear FM components, the TFD generates unwanted artefacts, also known as the cross-terms, which make the TFD interpretation even more challenging. Classical TFD processing methods rely on the fact that highly oscillatory cross-terms are located away from the origin of the signal ambiguity function (AF), hence they can be filtered out by low-pass filters.

One of the recently proposed methods for the cross-terms suppression uses the signal sparsity constraint, and it is based on compressive sensing (CS) of the samples near the signal AF origin. The number of CS samples is relatively small when compared to the total number of available samples. Thus, in order to obtain a high-resolution TFD, one needs to reconstruct it by solving an optimisation problem. The TFD is inherently sparse, containing only the trajectories of the signal components IF laws. Hence, by setting a sparsity inducing function as an objective function of this optimisation problem, one can obtain a high-resolution TFD.

The main goal of the proposed research is to increase the efficiency of the TFD reconstruction method by considering higher-order ambiguity functions, supplemented by the accompanying adaptive reconstruction algorithms. A TFD reconstruction algorithm based on the localised Rényi entropy is being developed, whose performance closely matches that of the state-of-the-art equivalents.