Fractional Fourier Transform Filtering Program
The Fractional Fourier Transform (FRFT) serves as a generalized form of the Fourier transform, exhibiting excellent energy concentration properties for Linear Frequency Modulated (LFM) signals where both time and frequency domains can be considered special cases of the FRFT domain. As illustrated in Figure 2, LFM signal projections across different transform domains show energy distributed widely in frequency domain while converging to an impulse function in the appropriate fractional Fourier domain. Being a linear transformation, the FRFT of a signal-noise mixture equals the superposition of their individual FRFTs. These properties enable effective LFM signal filtering in the FRFT domain. Key implementation involves scanning through rotation angles to compute fractional Fourier transforms of observed signals, generating two-dimensional energy distributions in parameter space for LFM detection with unknown parameters.