A Novel Algorithm for Linear Fractional Convolution

A novel algorithm based on fractional Fourier circular convolution theorem is proposed to deal with the fractional linear convolution, which is in accordance with the hidden periodicity of the discrete fractional Fourier transform. In the pre-processing, it applies the methods of overlap-save and overlap-add to make segment on the longer sequence. The algorithm is able to overcome the disadvantages of traditional fractional circular convolution theorem, which only can be used to calculate the convolution of two sequences with the similar length. Simulation results show the effectiveness of this algorithm.