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The fractional Fourier transform (FrFT), which is a generalized form of the well-known Fourier transform, has only recently started to appear in the field of signal processing. This has opened up the possibility of a new range of potentially promising and useful applications. In this letter, we develop a new FrFT-based chirp scaling algorithm (CSA) and compare its performance with the classical CSA based on the fast Fourier transform (FFT). Simulation results show that the FrFT-based CSA can offer significantly enhanced features compared to the classical FFT-based approach.