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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| Published in | Applicable analysis Vol. 86; no. 5; pp. 577 - 609 |
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| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.05.2007
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0003-6811 1563-504X |
| DOI | 10.1080/00036810701286288 |
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| 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. |
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| AbstractList | 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. |
| Author | Takei, Yoshitsugu Fujita, Keiko Berenstein, Carlos A. Morimoto, Akira Morimoto, Mitsuo Ashino, Ryuichi Napoletani, Domenico |
| Author_xml | – sequence: 1 givenname: Ryuichi surname: Ashino fullname: Ashino, Ryuichi organization: Mathematical Sciences , Osaka Kyoiku University – sequence: 2 givenname: Carlos A. surname: Berenstein fullname: Berenstein, Carlos A. organization: Institute for Systems Research, University of Maryland – sequence: 3 givenname: Keiko surname: Fujita fullname: Fujita, Keiko email: keiko@cc.saga-u.ac.jp organization: Faculty of Culture and Education, Saga University – sequence: 4 givenname: Akira surname: Morimoto fullname: Morimoto, Akira organization: Information Science , Osaka Kyoiku University – sequence: 5 givenname: Mitsuo surname: Morimoto fullname: Morimoto, Mitsuo organization: Division of Natural Sciences , International Christian University – sequence: 6 givenname: Domenico surname: Napoletani fullname: Napoletani, Domenico organization: School of Computational Sciences , George Mason University – sequence: 7 givenname: Yoshitsugu surname: Takei fullname: Takei, Yoshitsugu organization: Research Institute for Mathematical Sciences , Kyoto University |
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| Cites_doi | 10.1002/0470845899 10.1109/TSP.2004.828896 10.1049/el:20000623 10.1162/0899766054322964 10.1002/0471221317 10.1162/089976604773717586 10.1162/089976601300014385 |
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| Snippet | 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... |
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| SubjectTerms | 2000 Mathematics Subject Classifications: Primary: 94A12 Blind source separation Secondary: 42C40 Time-frequency analysis Wavelet |
| Title | Mathematical background for a method on quotient signal decomposition |
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