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The new magnitude-squared coherence functions and their properties sensitive to phase
1Department of Biomedical Engineering, Chongqing University of Medical Sciences, Chongqing, 400016 China.
Summary
This study introduces two new magnitude-squared coherence functions (MSCFs) to analyze signal coherence and phase relationships. These MSCFs reveal frequency domain coherence and phase properties between signals.
Area of Science:
- Signal Processing
- Data Analysis
Background:
- Coherence analysis is crucial for understanding relationships between signals.
- Existing methods may not fully capture phase-dependent information.
Purpose of the Study:
- To introduce novel magnitude-squared coherence functions (MSCFs).
- To investigate the phase sensitivity of these new MSCFs.
- To establish conditions for MSCFs to equal 1 or 0.
Main Methods:
- Leveraging the double spectral theorem from frequency domain coherence.
- Developing and analyzing two new types of MSCFs.
- Examining the impact of initial phases and phase differences on MSCFs.
Main Results:
- The proposed MSCFs effectively extract coherence between two signals.
- Two distinct MSCFs were presented, with conditions for values of 1 or 0.
- Both MSCFs demonstrate sensitivity to phase properties, reflecting frequency domain coherence and signal phase relationships.
Conclusions:
- The novel MSCFs provide insights into both frequency domain coherence and phase dynamics.
- One MSCF is sensitive to phase differences, while the other is sensitive to initial phases or phase differences.
- These findings enhance the understanding of signal relationships through phase-sensitive coherence analysis.
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