Fractional Fourier Transform with MATLAB Implementation for Chirp Signal Analysis

This MATLAB program implements Fractional Fourier Transform (FRFT) specifically designed for chirp signal processing. The FRFT represents a generalized Fourier transform approach that extends traditional Fourier analysis to handle non-stationary signals effectively. The implementation employs discrete FRFT algorithms using kernel matrix multiplication or decomposition methods, with optimized computational efficiency for handling chirp signals' linear frequency modulation characteristics. Key implementation features include: - Chirp signal generation with customizable parameters (start/end frequencies, duration) - Fractional order parameter control for flexible time-frequency analysis - Efficient matrix-based computation utilizing MATLAB's built-in linear algebra functions - Visualization routines for time-frequency representation and transformed signal analysis The program effectively transforms chirp signals into the fractional Fourier domain, enabling precise extraction of frequency modulation features. Through FRFT application, researchers can achieve comprehensive spectral characterization of chirp signals, facilitating deeper investigation of their time-frequency properties and supporting advanced signal processing applications in radar, communications, and acoustic analysis.