Discrete Time Convolution is Multiplication without Carry

Abstract

In this paper an analysis of discrete-time convolution is performed to prove that the convolution sum is polynomial multiplication without carry, whether the sequences are finite or not, by using several examples to compare the results computed using the existing approaches to the polynomial multiplication approach presented here. In the design and analysis of signals and systems the concept of convolution is very important. While software tools are available for calculating convolution, for proper understanding it is important to learn now to calculate it by hand. To this end, several popular methods are available. The idea that the convolution sum is indeed polynomial multiplication without carry is demonstrated in this paper. The concept is further extended to deconvolution, N-point circular convolution and the Z-transform approach.