1 A New Affine Fractional Fourier Transform With Circular Convolution Property

The fractional Fourier transform is a ubiquitous signal processing tool in basic and applied sciences and generalizes the Fourier transform. The convolution property of the discrete Fourier transform (DFT) is critical in its applications in electrical engineering, optics, and signal processing. We define a version of the discrete fractional Fourier transform (DFRFT) for which the circular convolution property holds. The proposed DFRFT is versatile, generalizes the DFT, and offers novel solutions to various time-varying signal processing problems. We further develop a fast computation method for the DFRFT based on chirp-z transform and show a chirp estimation method and confirm the results with simulations.