Phase Difference Detection Using Hilbert Transform and Wavelet Transform with MATLAB Implementation

This document explores the application of Hilbert Transform and Wavelet Transform for phase difference detection in signal processing. Both transforms serve as powerful mathematical tools for extracting phase information from signals. In MATLAB implementation, the Hilbert Transform can be applied using the built-in hilbert function, which returns an analytic signal from which instantaneous phase can be derived through angle calculation. For wavelet analysis, the Wavelet Toolbox provides functions like cwt (continuous wavelet transform) that enable time-frequency phase analysis through complex Morlet wavelets. The core algorithm involves computing the phase difference between two signals by comparing their instantaneous phases obtained from either transform. Key implementation steps include signal preprocessing, transform application, phase extraction using angle or unwrap functions, and phase difference calculation. These methods find extensive applications in signal processing and image analysis domains, particularly for analyzing complex signal patterns and image features. Mastering the principles and implementation techniques of these transforms significantly enhances research capabilities and practical applications in these fields, with MATLAB providing robust computational frameworks for both theoretical validation and real-world deployment.