The fractional Fourier transform and its application to high resolution SAR imaging

The fractional Fourier transform (FrFT), which is a generalized form of the well-known Fourier transform, has opened up the possibility of a new range of potentially promising and useful applications including radar involving the use and detection of chirp signals, pattern recognition and Synthetic Aperture Radar (SAR) image processing. The Chirp Scaling Algorithm (CSA) is one of the most important and well-known radar imaging algorithms. It is attractive because of its excellent focusing ability and implementation simplicity. Benefiting from the inherent structure of the FrFT for non- stationary digital signal processing and analysis, especially for chirped-type signals, a new version of the CSA based on the Fractional Fourier Transform (FrFT) is developed. The introduced Fractional Chirp Scaling Algorithm (FrCSA) applied the Fast Fourier Transform (FFT) instead of the fractional Fourier transform (FrFT) in the azimuth direction for the analytical development tractability purposes only as it numerically tractable in both dimensions. To demonstrate the resolution and focusing enhancement in the azimuth dimension using the FrCSA and also to be able to perform azimuth fractional filtering, noise removal and flight path nonlinearity compensation, a closed form expression for the azimuth fractional transformation is required. In this talk we present the mathematical derivation for a closed- form expression of the azimuth-fractional Fourier transform of the new FrCSA with application to high resolution imaging. Results to real SAR data images will show significantly enhanced features using the FrFT-based azimuth expression instead of the classical FFT-based one within the fractional chirp scaling algorithm or any other chirped-type SAR imaging algorithm.