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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2008 E91-A(3):791-800; doi:10.1093/ietfec/e91-a.3.791
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Copyright © 2008 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Papers -- Digital Signal Processing

A Sparse Decomposition Method for Periodic Signal Mixtures

Makoto NAKASHIZUKA1

1 The author is with the Graduate School of Engineering Science, Osaka University, Toyonaka-shi, 560-8531 Japan. E-mail: nkszk{at}sys.es.osaka-u.ac.jp


  Abstract

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.

Key Words: periodic structures, sparse representation, estimation, signal resolution, relaxation method

Manuscript received April 23, 2007. Manuscript revised October 4, 2007.


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