Mathematical background for a method on quotient signal decomposition

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...

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Bibliographic Details
Published inApplicable analysis Vol. 86; no. 5; pp. 577 - 609
Main Authors Ashino, Ryuichi, Berenstein, Carlos A., Fujita, Keiko, Morimoto, Akira, Morimoto, Mitsuo, Napoletani, Domenico, Takei, Yoshitsugu
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.05.2007
Subjects
2000 Mathematics Subject Classifications: Primary: 94A12
Blind source separation
Secondary: 42C40
Time-frequency analysis
Wavelet
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ISSN0003-6811
1563-504X
DOI10.1080/00036810701286288

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Summary: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.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036810701286288