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Double Spectral theorem and Two Type Magnitude-Squared Coherence Functions

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7 Author(s)
Xie, Z.X. ; Coll. of Bioinformatics, Chongqing Univ. of Post & Telecommun. ; Li, H. ; Xie, D.M. ; Li, Z.Y.
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Studying frequency domain representation for the coherence between two signals is an important basic theoretical problem in the fundamental theories of signal processing. However, the old magnitude-squared coherence function (OMSCF) has been proved identical to 1, so that to cannot be used to extract any coherence information. Here, we will prove a core theorem in frequency domain coherence theories in signal processing, called as the double spectral theorem (DST). Based on the theorem, we presented the two types of new magnitude-squared coherence functions (MSCFs), called as the same type magnitude-squared coherence function (SMSCF) and the difference magnitude-squared coherence function (DMSCF) respectively, which were mathematically derived from DST and the conditions that they are equal to 1 or 0 can be theoretically derived from DST. Here, we further demonstrated that SMSCF and DMSCF could be used to exactly extract the coherence between two signals by each component

Published in:

Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference of the

Date of Conference:

17-18 Jan. 2006

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