A Signal-Dependent Time-Frequency Representation: Fast Algorithm for Optimal Kernel Design

Richard G. Baraniuk; Douglas L. Jones

doi:10.1109/78.258128

A Signal-Dependent Time-Frequency Representation: Fast Algorithm for Optimal Kernel Design

Richard G. Baraniuk, Douglas L. Jones

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

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(Q log Q), 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.

Original language	English (US)
Pages (from-to)	134-146
Number of pages	13
Journal	IEEE Transactions on Signal Processing
Volume	42
Issue number	1
DOIs	https://doi.org/10.1109/78.258128
State	Published - Jan 1994

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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title = "A Signal-Dependent Time-Frequency Representation: Fast Algorithm for Optimal Kernel Design",

abstract = "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(Q log Q), 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.",

author = "Baraniuk, {Richard G.} and Jones, {Douglas L.}",

note = "Funding Information: Manuscript received December 24, 1991; revised August 19, 1992. The associate editor coordinating the review of this paper and approving it for publication was Prof. Georgios B. Giannakis. This work was supported by the Sound Group of the Computer-based Education Research Laboratory, University of Illinois, the Joint Services Electronics Program under Grant N00014-90-J-1270, and the National Science Foundation under Grant MIP-90-12747. R. G. Baraniuk is with the Department of Electrical and Computer Engineering, Rice University, Houston, TX 7725 1-1992. D. L. Jones is with the Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801. IEEE Log Number 9213274. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",

year = "1994",

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A Signal-Dependent Time-Frequency Representation: Fast Algorithm for Optimal Kernel Design

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