A SIGNAL-DEPENDENT TIME-FREQUENCY REPRESENTATION - FAST ALGORITHM FOR OPTIMAL KERNEL DESIGN

A time frequency representation based on an optimal, signal dependent kernel has been proposed recently in an attempt to overcome one of the primary limitations of bilinear time-frequency distributions: that the best kernel and distribution depend on the signal to be analyzed. The optimization formulation for the signal dependent kernel results in a linear program with a unique feature: a tree structure that summarizes a set of constraints on the kernel. In this paper, we present a fast algorithm based on sorting to solve a special class of linear programs that includes the problem of interest. For a kernel with Q variables, the running time of the algorithm is O(QlogQ), which is several orders of magnitude less than any other known method for solving this class of linear programs. This efficiency enables the computation of the signal-dependent, optimal-kernel time-frequency representation at a cost that is on the same order as a fixed-kernel distribution. An important property of the optimal kernel is that it takes on essentially only the values of 1 and 0.