Computing the Convolution of Analog and Discrete Time Exponential Signals Algebraically

TL;DR

This paper introduces an algebraic method for computing the convolution of exponential signals using linear algebra, specifically Vandermonde matrices, avoiding integrals or summations, and applies it to differential and difference equations.

Contribution

The paper presents a novel algebraic procedure for convolution of exponential signals that bypasses traditional integral or summation calculations, utilizing Vandermonde matrices.

Findings

Convolution can be computed algebraically using Vandermonde matrices.

The method simplifies solving differential and difference equations with exponential signals.

The approach avoids complex integral or summation calculations.

Abstract

We present a procedure for computing the convolution of exponential signals without the need of solving integrals or summations. The procedure requires the resolution of a system of linear equations involving Vandermonde matrices. We apply the method to solve ordinary differential/difference equations with constant coefficients.