Parameter Estimation Processing of Multi-component LFM Signals Using Fractional Fourier Transform

The Fractional Fourier Transform (FrFT) serves as an effective processing method for parameter estimation of multi-component Linear Frequency Modulated (LFM) signals. This technique decomposes and reconstructs signals to extract frequency and amplitude information through rotational operations in the time-frequency plane. The implementation typically involves calculating the optimal fractional order that maximizes energy concentration in the FrFT domain. During processing, we first apply the Fractional Fourier Transform to LFM signals using discrete computation algorithms, which can be implemented through matrix multiplication or fast computation methods similar to FFT. Subsequently, parameter estimation is performed based on the transformed results by identifying peak positions in the fractional Fourier domain corresponding to chirp rates and center frequencies. Code implementation often involves optimizing the fractional order parameter using search algorithms and applying peak detection techniques to extract signal components. This approach enables more accurate acquisition of LFM signal parameters, thereby facilitating more precise signal analysis and processing through mathematical operations like component separation and reconstruction.