MATLAB Implementation and Visualization of Autocorrelation and Cross-Correlation Functions

Autocorrelation and cross-correlation functions are fundamental tools in signal processing, widely used for analyzing signal periodicity and correlations between different signals. In MATLAB, these functions can be computed using the xcorr function for discrete signals and the xcov function for continuous signals. The xcorr function calculates the correlation between two sequences with optional parameters for normalization and maximum lag specification. For visualization, MATLAB provides the plot function for continuous representations and the stem function for discrete signal displays, allowing clear graphical interpretation of correlation results. When implementing these calculations, it's crucial to perform signal standardization first using z-score normalization or min-max scaling to prevent amplitude-related biases in the results. The typical implementation involves: 1) Normalizing input signals using (signal-mean(signal))/std(signal), 2) Computing correlations with xcorr(signal1, signal2, 'coeff') for normalized results, and 3) Visualizing with stem(lags, correlation) for discrete signals or plot() for continuous representations. This approach ensures accurate correlation analysis independent of signal magnitude variations.