MATLAB Program for Cyclic Cross-Correlation of Cyclostationary Time Series

This MATLAB program calculates cyclic cross-correlation for cyclostationary time series. Cyclostationary time series represent a crucial concept in statistics and time series analysis, characterized by statistical properties (mean and variance) that remain periodic over time rather than constant. The implementation employs cyclic cross-correlation to measure the relationship between two time series, distinguishing it from conventional cross-correlation by incorporating cyclic shifting operations during computation. This approach effectively captures periodic dependencies between signals, making it particularly valuable for analyzing seasonal patterns, communication signals, and mechanical vibration data. The program utilizes MATLAB's signal processing capabilities to implement cyclic shifting through circular permutation algorithms, typically employing modulus operations and array indexing techniques. Key computational steps include: 1) Preprocessing input sequences to ensure equal length handling, 2) Implementing cyclic shifts using circshift functions or custom modulo-based indexing, 3) Calculating correlation coefficients for each shift position through vectorized operations. Researchers can leverage this tool to investigate periodic relationships in signals, with applications in telecommunications (signal detection), finance (seasonal trends), and mechanical systems (vibration analysis). The code structure allows customization of shift parameters and correlation methods, facilitating deeper exploration of time series characteristics and underlying patterns.