Fractional Fourier Transform (FrFT) for Linear Frequency Modulation Signal Parameter Estimation

The Fractional Fourier Transform (FrFT) is a mathematical method used for parameter estimation of Linear Frequency Modulation (LFM) signals, specifically for determining chirp rate and initial frequency. This implementation employs a coarse-to-fine search strategy to optimize the fractional order parameter of the transform. To utilize this method, you need to download the frft.m utility function from online sources and integrate it into your MATLAB codebase. This function implements the core FrFT algorithm using spectral decomposition or discrete implementation approaches, typically involving eigenvalue decomposition of the Fourier operator. The parameter estimation process works by iteratively testing different fractional orders through the frft.m function, where the optimal order corresponds to the maximum energy concentration in the FrFT domain. When properly tuned, the FrFT can precisely identify the chirp rate through the fractional order relationship and extract initial frequency from the peak position in the transformed domain, significantly improving signal processing accuracy for LFM signals compared to conventional Fourier analysis. Key implementation steps include: initial coarse search over a wide order range (e.g., 0.1 increments), followed by refined search around promising orders (e.g., 0.01 increments), with peak detection algorithms applied to the FrFT output magnitude to identify optimal parameters.