A Sparse Decomposition Method for Periodic Signal Mixtures

Makoto NAKASHIZUKA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.3   pp.791-800
Publication Date: 2008/03/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.3.791
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
periodic structures,  sparse representation,  estimation,  signal resolution,  relaxation method,  

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Summary: 
This study proposes a method to decompose a signal into a set of periodic signals. The proposed decomposition method imposes a penalty on the resultant periodic subsignals in order to improve the sparsity of decomposition and avoid the overestimation of periods. This penalty is defined as the weighted sum of the l2 norms of the resultant periodic subsignals. This decomposition is approximated by an unconstrained minimization problem. In order to solve this problem, a relaxation algorithm is applied. In the experiments, decomposition results are presented to demonstrate the simultaneous detection of periods and waveforms hidden in signal mixtures.