Cross-Correlation Function Calculation for Two Sequences: Implementation and Noise Analysis

In signal processing applications, we frequently need to compute cross-correlation functions between two sequences or auto-correlation functions for individual sequences. The cross-correlation function serves to analyze the correlation relationship between two signals, while the auto-correlation function examines internal correlations within a single signal. These functions are fundamental tools for applications including signal filtering, spectral analysis, and pattern recognition. From an implementation perspective, MATLAB's xcorr function provides efficient computation of these correlations, with algorithms typically utilizing FFT-based methods for optimal performance with large datasets. Additionally, by conducting correlation analysis under different noise power conditions, we can demonstrate how noise levels impact the accuracy and reliability of correlation results, which is crucial for practical signal processing scenarios where noise resilience is a key consideration.