Fractional Fourier Transform: MATLAB Simulation for Single-Component LFM Signal Detection and Parameter Estimation

This article explores the MATLAB simulation implementation of fractional Fourier transform (FrFT), specifically applied to the detection and parameter estimation of single-component linear frequency modulation (LFM) signals. The fractional Fourier transform represents an advanced signal processing technique that provides superior characterization of non-stationary signal properties. This method has gained significant attention in signal processing applications, with continuous improvements and refinements in implementation approaches.

We provide detailed explanations of the theoretical foundations of fractional Fourier transform alongside comprehensive MATLAB implementation guidelines. The implementation typically involves constructing rotation operators in the time-frequency plane using discrete fractional Fourier transform algorithms, which can be coded using built-in MATLAB functions or custom optimization routines. Key implementation aspects include proper sampling rate selection, order parameter optimization, and computational efficiency improvements through vectorization techniques.

The article specifically examines applications for single-component LFM signal detection and parameter estimation, demonstrating how fractional Fourier transform enhances these processes through peak detection algorithms in the fractional Fourier domain. The MATLAB code implementation typically involves signal preprocessing, FrFT computation at optimal orders, and parameter extraction using maximum energy concentration principles. We illustrate how to implement chirp rate estimation and initial frequency calculation through coordinate rotation and energy distribution analysis in the transformed domain.

This comprehensive discussion aims to contribute to both research and practical applications of fractional Fourier transform, providing implementable MATLAB solutions with detailed code structure explanations for international technical audiences.