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Adaptive time-frequency representations for multiple structures

We propose an adaptive quadratic time-frequency representation (QTFR) based on a matching pursuit signal decomposition that uses a dictionary with elements matched to the instantaneous frequency of the analysis signal components. We form the QTFR as a weighted linear superposition of QTFRs chosen by the algorithm to provide a highly localized representation for each of the adaptively selected dictionary elements. This is advantageous as the resulting representations are parsimonious and reduce the effect of cross terms. Also, they exhibit maximum time-frequency localization for the difficult analysis case of signals with multiple components that have different time-frequency characteristics. Thus, the new technique can be used to analyze and classify multi-structure signal components as demonstrated by our synthetic and real data simulation examples.