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Double spectral theorem and two type magnitude-squared coherence functions.

Research paper by Z X ZX Xie, H H Li, D M DM Xie, Z Y ZY Li, X F XF Zhong, Z F ZF Wang, Y H YH Liu

Indexed on: 07 Feb '07Published on: 07 Feb '07Published in: Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference



Abstract

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.

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