A Technique for Computing the Convolution of Exponential Signals and its Application in Systems Theory

We present a procedure for computing the convolution of (analog-time) exponential signals without the need of solving integrals. The procedure is algebraic and requires the resolution of a system of linear equations. The method can be applied to find the impulse response of a linear time-invariant (LTI) system modeled by an ordinary differential equation and also to compute the solution of an ordinary differential equation with constant coefficients. We believe this technique can be useful for the analysis of LTI systems in time domain, since it is conceptually simple and can be easily implemented as algorithms in software packages like Scilab and/or Matlab.