A SIGNAL-DEPENDENT TIME-FREQUENCY REPRESENTATION - OPTIMAL KERNEL DESIGN

Time-frequency distributions (TFD's), which indicate the energy conten t of a signal as a function of both time and frequency, are powerful t ools for time-varying signal analysis. The lack of a single distributi on that is ''best'' for all applications has resulted in a proliferati on of TFD's, each corresponding to a different, fixed mapping from sig nals to the time-frequency plane. A major drawback of all fixed mappin gs is that, for each mapping, the resulting time-frequency representat ion is satisfactory only for a limited class of signals. In this paper , we introduce a new TFD that adapts to each signal and so offers good performance for a large class of signals. The design of the signal-de pendent 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, he nce, the optimal time-frequency mapping for that signal. A fast algori thm has been developed for solving the linear program, allowing the co mputation of the signal-dependent TFD with a time complexity on the sa me order as a fixed-kernel distribution. Besides this computational ef ficiency, an attractive feature of the optimization-based approach is the ease with which the formulation can be customized to incorporate a pplication-specific knowledge into the design process.