Cross-term-free time-frequency distribution reconstruction via lifted projections
Date
2015-01Source Title
IEEE Transactions on Aerospace and Electronic Systems
Print ISSN
0018-9251
Publisher
Institute of Electrical and Electronics Engineers
Volume
51
Issue
1
Pages
479 - 491
Language
English
Type
ArticleItem Usage Stats
220
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227
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Abstract
A crucial aspect of time-frequency (TF) analysis is the identification of separate components in a multicomponent signal. The Wigner-Ville distribution is the classical tool for representing such signals, but it suffers from cross-terms. Other methods, which are members of Cohen's class of distributions, also aim to remove the cross-terms by masking the ambiguity function (AF), but they result in reduced resolution. Most practical time-varying signals are in the form of weighted trajectories on the TF plane, and many others are sparse in nature. Therefore, in recent studies the problem is cast as TF distribution reconstruction using a subset of AF domain coefficients and sparsity assumption. Sparsity can be achieved by constraining or minimizing the l(1) norm. In this article, an l(1) minimization approach based on projections onto convex sets is proposed to obtain a high-resolution, cross-term-free TF distribution for a given signal. The new method does not require any parameter adjustment to obtain a solution. Experimental results are presented.
Keywords
Fourier - transformWigner distribution
Signature analysis
Fault - detection
Stator current
Radar
Algorithm
Signals
Representations
Information