Open AccessDiscrete Time Convolution is Multiplication without Carry
Author(s) -
Innocent E. Okoloko
Publication year - 2021
Publication title -
european journal of electrical engineering and computer science
Language(s) - English
Resource type - Journals
ISSN - 2736-5751
DOI - 10.24018/ejece.2021.5.5.358
Subject(s) - convolution (computer science) , multiplication (music) , deconvolution , carry (investment) , circular convolution , convolution power , overlap–add method , polynomial , convolution theorem , mathematics , computer science , arithmetic , algorithm , algebra over a field , pure mathematics , fourier transform , mathematical analysis , artificial intelligence , combinatorics , fourier analysis , finance , artificial neural network , fractional fourier transform , economics
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.