Wigner Transform Analysis of Single-Pulse, LFM, and BPSK Radar Signals

This code performs Wigner-Ville distribution (WVD) analysis on three radar signal types: conventional single-pulse radar signals, Linear Frequency Modulated (LFM) radar signals, and Binary Phase Shift Keying (BPSK) radar signals to generate their time-frequency representations. The Wigner transform is a fundamental mathematical tool in signal processing that simultaneously displays temporal and spectral characteristics, allowing for detailed examination of how signal energy distributes across time-frequency planes. The implementation involves generating baseband equivalents of each radar signal type with proper parameterization: single-pulse signals with rectangular envelopes, LFM signals with linear frequency sweeps, and BPSK signals with phase transitions. The core algorithm computes the analytic signal using Hilbert transform before applying the WVD calculation through quadratic time-frequency distribution methods. Key MATLAB functions include `hilbert()` for analytic signal generation and custom WVD computation loops that handle cross-term suppression for multi-component signals. Through this Wigner transform analysis, we can investigate unique time-frequency features: single-pulse signals show concentrated energy in short durations, LFM signals demonstrate linear time-frequency trajectories, and BPSK signals reveal phase-induced instantaneous frequency jumps. This comparative study provides insights into their respective advantages for different radar applications, contributing to signal selection and waveform design in modern radar systems. The time-frequency analysis methodology implemented here supports advanced radar signal processing research and development.