Fractional Chirp Scaling Algorithm: Mathematical Model

In this paper, the new fractional chirp scaling algorithm (FrCSA) is mathematically derived and analyzed from high-resolution SAR imaging point of view. The FrCSA is based on the use of the fractional Fourier transform within the chirp scaling algorithm (CSA). The performance of the FrCSA is compared to that of the classical CSA that is based on the fast Fourier transform (FFT). Simulation results for airborne SAR systems show that the FrCSA offers enhanced signal-to-noise ratio (SNR), better focusing capabilities, sharpened main lobe with extra power concentration, and greater side-lobe reduction ratio (SLRR) and all of these, without the need for any additional focusing or enhancement techniques that are required in the classical FFT-based CSA.