Implementation of Hilbert Transform in Signal Processing

This program implements the Hilbert transform for signal processing applications, developed on the MATLAB platform. The implementation utilizes MATLAB's built-in hilbert() function to convert signals from the time domain to the analytic signal representation in the frequency domain. The algorithm works by computing the Fourier transform of the input signal, zeroing out negative frequency components, and applying the inverse Fourier transform to obtain the analytic signal. Through this program, we can effectively analyze the spectral characteristics of signals and extract meaningful frequency information. The implementation includes parameter configuration for windowing functions and sampling rate adjustments to optimize spectral resolution. Being developed on MATLAB, this program offers excellent scalability and user-friendly operation through its interactive GUI and script-based interface. In practical applications, this implementation can be utilized in audio processing for envelope detection and instantaneous frequency analysis, as well as in image processing for Hilbert transform-based edge detection. The program also includes visualization features for plotting original signals, transformed signals, and their spectral representations. Overall, this Hilbert transform implementation serves as a valuable tool for in-depth study and understanding of signal processing concepts, particularly in time-frequency analysis and complex signal manipulation.