Analysis of LFM Signals Using Fractional Fourier Transform (FRFT)

In applications of Linear Frequency Modulated (LFM) signals, LFM is extensively utilized across various information systems as a classic non-stationary signal characterized by large time-bandwidth product. From electronic warfare and electronic countermeasures perspectives, LFM signals are typically adopted to address the trade-off between operating range and range resolution while improving signal stealth. Consequently, the detection and parameter estimation of LFM signals have become crucial research areas in electronic warfare. The MATLAB implementation employs Fractional Fourier Transform (FRFT) for precise LFM parameter estimation, achieving highly accurate results. The algorithm operates by rotating the time-frequency plane to optimally concentrate LFM energy at a specific fractional order, where parameters like chirp rate and initial frequency can be extracted through peak detection in the FRFT domain. Our routine demonstrates this process through MATLAB's signal processing toolbox functions, including custom FRFT implementation using discrete sampling methods and optimization techniques for order selection. The following example code illustrates FRFT computation in MATLAB, complete with operational results showing clear energy concentration at the optimal transform order.