Applications of ambiguity function-based kernels in time-frequency representations

Time-Frequency Representations (TFRs) are useful tools for the analysis of non-stationary signals. However, a single TFR can not be considered optimum for all kinds of signals. This fact has motivated the development of a general optimization procedure to obtain a kernel specially matched to the signal under analysis. The procedure has two shortcomings: its computational complexity and its dependence on a parameter that is difficult to choose. In order to avoid this heavy procedure, this work proposes the use of TFR kernels based on the absolute value of the ambiguity function to obtain attributes related to the physical processes that generate the signals. The concept is applied to noise reduction in monocomponent signals combinations, determination of layer depth in reflection seismology, pitch contour extraction from speech signals and location of evoked potentials in brain signals. Experiments were performed using simulated and real signals. In each case, the selected kernel preserves the relevant information with minimum loss of resolution, and minimizes the cross-terms and other impurities that may affect the signal, thus demonstrating the effectiveness of the proposed method