Mathematical background for a method on quotient signal decomposition

Abstract

The blind source separation problem is discussed in this article. Focusing on the assumption of independency of the sources in the time-frequency domain, we present a mathematical formulation for the estimation problem of the number of sources. The proposed method uses the quotient of complex valued time-frequency information of only two observed signals to detect the number of sources. No fewer number of observed signals than the detected number of sources is needed to separate sources. The assumption on sources is quite general independence in the time-frequency plane, which is different from that of independent component analysis. We propose algorithms with feedback and give numerical simulations to show the method works well even for noisy case.

Keywords:

• Blind source separation
• Time-frequency analysis
• Wavelet

Keywords:

• 2000 Mathematics Subject Classifications: Primary: 94A12
• Secondary: 42C40

Acknowledgements

This work was supported by the Japan Society for the Promotion of Science for a Japan–U.S. Cooperative Science Program (2003.4–2005.3). C. A. Berenstein was also supported in part by NSF Grant DMS-0400698. K. Fujita also thanks to the Research Institute for Mathematical Sciences of Kyoto University for giving her an opportunity to stay there (2004.7–2005.2) and to do this research.