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. >

介绍了一种新的时频分布（TFD），它能适应每种信号，因此对一大类信号都有良好的性能。这种依赖于信号的时频分布的设计在科恩类中被表述为一个优化问题，并产生一个特殊的线性规划。给定一个要分析的信号，该线性规划的解产生最优核，从而得到该信号的最优时频映射。已经开发出一种快速算法来求解这个线性规划，使得依赖于信号的时频分布的计算时间复杂度与固定核分布处于同一数量级。除了这种计算效率外，基于优化的方法的一个吸引人的特点是，其公式很容易定制，以便将特定应用的知识纳入设计过程。