A signal-dependent time-frequency representation: optimal kernel design

A new time-frequency distribution (TFD) that adapts to each signal and so offers a good performance for a large class of signals is introduced. The design of the signal-dependent TFD is formulated in Cohen's class as an optimization problem and results in a special linear program. Given a signal to be analyzed, the solution to the linear program yields the optimal kernel and, hence, the optimal time-frequency mapping for that signal. A fast algorithm has been developed for solving the linear program, allowing the computation of the signal-dependent TFD with a time complexity on the same order as a fixed-kernel distribution. Besides this computational efficiency, an attractive feature of the optimization-based approach is the ease with which the formulation can be customized to incorporate application-specific knowledge into the design process.<
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