Fractional Fourier Transform of Chirp Signals

This research implements the Fractional Fourier Transform (FrFT) for chirp signals and demonstrates their characteristic energy concentration property. The implementation utilizes the discrete FrFT algorithm based on eigenvalue decomposition of the Fourier operator, where chirp signals show optimal energy compaction at specific fractional orders. Additionally, we applied FrFT to analyze single-frequency signals (revealing rotation properties in time-frequency plane), multi-frequency components (demonstrating separation capabilities), and Gaussian signals (showing invariance under FrFT operations). These analyses provide deeper insights into spectral characteristics and energy distribution patterns of various signal types. The MATLAB implementation involves key functions for angle parameterization, eigenvector computation, and fractional order optimization. These findings hold significant value for advanced signal processing applications including time-frequency analysis, signal compression, and non-stationary signal detection.