On Convolution and Product Theorems for FRFT

The fractional Fourier transform (FRFT), which is considered as a generalization of the Fourier transform (FT), has emerged as a very efficient mathematical tool in signal processing for signals which are having time-dependent frequency component. Many properties of this transform are already known, but the generalization of convolution theorem of Fourier transform for FRFT is still not having a widely accepted closed form expression. In the recent past, different authors have tried to formulate convolution theorem for FRFT, but none have received acclamation because their definition do not generalize very appropriately the classical result for the FT. A modified convolution theorem for FRFT is proposed in this article which is compared with the existing ones and found to be a better and befitting proposition.