Phase Difference Detection of Correlated Signals

This document explores the problem of phase difference detection in correlated signals, which finds applications across multiple domains including communications, radar systems, and radio technology. The detection process involves sophisticated mathematical tools such as Fourier transform analysis and filter design methodologies. To validate our theoretical approach, we conducted simulation experiments using MATLAB. The simulation framework included designing multiple test cases with varying signal parameters and noise conditions. Key MATLAB functions employed in our implementation include fft() for frequency domain analysis, xcorr() for cross-correlation computation, and angle() for phase extraction. Through detailed analysis of simulation results, including quantitative performance metrics and error rate calculations, we confirmed the feasibility and accuracy of our proposed method. Future research directions may involve extending this approach to real-time signal processing applications and exploring adaptive algorithms for dynamic signal environments.