The new magnitude coherence functions and their properties sensitive to phase.

Because magnitude-squared coherence function (MSCFs) could lose some phase information, based on the core theorem for the frequency domain coherence in signal processing, called as double spectral theorem, we present the two types of new magnitude coherence functions (MCFs) in order to extract the coherence between two signals and give the conditions that they are equal to 0 or +1 or -1. Here, we further study their properties sensitive to initial phases of two signals and phase difference between two signals. Studying demonstrated that the two type MCFs not only reflect frequency domain coherence of two signals, but also reflect the phase relationship between two signals.

Double Spectral theorem and Two Type Magnitude Coherence Functions.

Studying frequency domain representation for the coherence between two signals is an important basic theoretical problem in the fundamental theories of signal processing. However, magnitude-squared coherence function (MSCFs) could lose some phase information. Based on the core theorem in the frequency domain coherence theories, called as double spectral theorem (DST), we presented the two types of new magnitude coherence functions (MCFs), called as the same type magnitude coherence function (SMCF) and the difference magnitude coherence function (DMCF) respectively, which had been mathematically derived from DST and the conditions that they are equal to 1 or -1 or 0 were theoretically derived from DST.