Copyright © 2008 The Institute of Electronics, Information and Communication Engineers
Regular Section -- Papers -- Digital Signal Processing |
A Sparse Decomposition Method for Periodic Signal Mixtures
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
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.
Reference
[1] J.R. Deller, J.H.L. Hansen, and J.G. Proakis, Discrete-Time Processing of Speech Signals, Wiley-Interscience. 1993. [2] B. Santhanam and P. Maragos, "Harmonic analysis and restoration of separation methods for periodic signal mixtures: Algebraic separation versus comb filtering," Signal Process., vol.69, no.1, pp.81–91, 1998. [3] W.A. Sethares and T.W. Staley, "Periodicity transform," IEEE Trans. Signal Process., vol.47, no.11, pp.2953–2964, Nov. 1999. [4] D.D. Muresan and T.W. Parks, "Orthogonal, exactly periodic subspace decomposition," IEEE Trans. Signal Process., vol.51, no.9, pp.2270–2279, Nov. 2003. [5] S. Mallat and Z. Zhang, "Matching pursuit in a time-frequency dictionary," IEEE Trans. Signal Process., vol.41, no.12, pp.3397–3415, Dec. 1993. [6] S.S. Chen, D.L. Donoho, and M.A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol.20, no.1, pp.33–61, 1998. [7] S. Sardy, A.G. Bruce, and P. Tseng, "Block coordinate relaxation methods for nonparametric wavelet denoising," J. Computational and Graphical Statistics, vol.9, no.2, pp.361–379, 2000. [8] J.L. Stark, M. Elad, and D.L. Donoho, "Image decomposition via the combination of sparse representations and a variational approach," IEEE Trans. Image Process., vol.14, no.10, pp.1570–1582, Oct. 2005. [9] A. de Cheveigne and H. Kawahara, "Multiple period estimation and pitch perception model," Speech Commun., vol.27, pp.175–185, 1999. [10] M. Wu, D. Wan, and G.J. Brown, "A multipitch tracking algorithm for noisy speech," IEEE Trans. Speech Audio Process., vol.11, no.3, pp.229–241, May 2003. [11] M. Goto, "A real-time music scene description system: Predominant-F0 estimation for detecting melody and bass lined in real-world audio signals," Speech Commun., vol.43, no.4, pp.311–329, 2004. [12] J.L. Roux, H. Kameoka, N. Ono, A. de Cheveigne, and S. Sagayama, "Single and multiple F0 contour estimation through parametric spectrogram modeling of speech in noisy environments," IEEE Trans. Audio, Speech and Language Processing, vol.15, no.4, pp.1135–1145, May 2007.
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