Azimuth fractional transformation of the fractional chirp scaling algorithm (FrCSA)

The fractional chirp scaling algorithm (FrCSA) is based on the use of the fractional Fourier transform (FrFT) within the chirp scaling algorithm (CSA). In this paper, a closed-form expression for the azimuth FrFT of the FrCSA is mathematically derived and analyzed from the high-resolution synthetic aperture radar imaging point of view. The azimuth-FrFT expression of the FrCSA is compared to that of the classical fast Fourier transform (FFT)-based CSA. As the FFT is a special case of the generalized FrFT, the derived expression is found to be in total agreement with that of the FFT-based CSA when the transformation order is equal to unity; that is the angle of rotation is equal to pi/2