Computational Methods of Fractional Fourier Transform: Algorithm Implementation and Code Examples

This article provides an in-depth examination of computational methods for the fractional Fourier transform (FRFT) and demonstrates its application in processing various signal types. We explore both discrete and continuous implementation approaches, including the decomposition method using ordinary Fourier transforms and direct computation via fractional Fourier operators. The discussion extends to practical application domains such as signal compression, time-frequency analysis, and communications systems, supported by real-world case studies. To facilitate understanding, we include comprehensive program listings featuring key functions like frft_calc() for transformation core computation and visualization routines for time-frequency representations. Practical code examples illustrate parameter optimization techniques and demonstrate how to handle different signal types including chirp signals and non-stationary processes. Through this material, readers will gain mastery of FRFT fundamentals, understand its practical significance in signal processing applications, and develop proficiency in implementing these methods to solve real-world engineering problems.