An algorithm to reduce the complexity required to convolve finite length sequences using the Hirschman optimal transform (HOT)

Abstract

We develop an algorithm suitable for convolving two finite length sequences of uneven length that is more efficient than its FFT-based competitor. In particular, we present a method for computing a fast linear convolution of the finite length sequences h and x where the length of x is much greater than the length of h using the Hirschman optimal transform (HOT). When compared to the most efficient methods using the DFT and its fast FFT implementation, our method can reduce the computational complexity by a third.