High-Precision Discrete Convolution Algorithm Based on Moments

Convolution is an important and useful operation in the fields of digital signal processing. In this paper, based on the previous work of performing discrete Fourier transform (DFT) via linear sums of discrete moments, we have made  development to eliminate multiplications in discrete Fourier transforms by performing appropriate bit operations and shift operations in binary system, which can be implemented by integer additions of fixed points; then using the convolution theorem with the DFT, we compute the convolution with two DFTs, a point-by-point product, and an inverse DFT. Our algorithm involves fewer multiplications and can deal with arbitrary length signals.