  The Fractional Fourier Transform is a ubiquitous signal processing tool in
basic and applied sciences. The Fractional Fourier Transform generalizes every
property and application of the Fourier Transform. Despite the practical
importance of the discrete fractional Fourier transform, its applications in
digital communications have been elusive. The convolution property of the
discrete Fourier transform plays a vital role in designing multi-carrier
modulation systems. Here we report a closed-form affine discrete fractional
Fourier transform and we show the circular convolution property for it. The
proposed approach is versatile and generalizes the discrete Fourier transform
and can find applications in Fourier based signal processing tools.
