MATLAB Code Implementation of Coherence Function

The coherence function is a tool used to analyze frequency-domain relationships between two signals, particularly widely utilized in signal processing and communication systems. It helps determine the degree of correlation between two signals in the frequency domain, typically ranging from 0 to 1, where 1 indicates perfect coherence and 0 represents no correlation.

Implementing the coherence function in MATLAB generally requires functions from the Signal Processing Toolbox. The fundamental approach involves calculating the cross-power spectral density of the two signals and their individual auto-power spectral densities, followed by normalization. Key functions often used include pwelch for power spectral density estimation and mscohere for direct coherence computation.

The implementation workflow typically includes these steps: First, segment the input signals and apply windowing (using functions like hamming or hann) to reduce spectral leakage. Then compute the Fourier transform for each segment and derive their power spectra. Subsequently, average the cross-power spectra and auto-power spectra across segments to minimize random errors, finally calculating coherence values. This Welch's method implementation provides statistical stability through periodogram averaging.

This implementation method is not only suitable for stationary signal analysis but can also be extended to non-stationary signal studies. In practical applications, coherence functions are commonly used in fault diagnosis, system identification, and communication system performance evaluation. By adjusting parameters such as window function types (e.g., Hanning, Hamming) and segment lengths, analysts can optimize the accuracy and frequency resolution of the results. The mscohere function in MATLAB automatically handles most of these computations with customizable parameters for overlap percentage and window size.