A systematic method for the analytical evaluation of convolution integrals

Analytic methods are presented for the systematic evaluation of convolution integrals that contain piecewise-continuous or piecewise-smooth functions. These methods involve breaking the convolution integral into a sum of integrals and expressing each integral in a standard form that can be easily evaluated. Mathematical insight is gained by looking at the result as a superposition of terms, where each term is nonzero or active during a specific time interval. Applications to both causal and noncausal linear systems are considered. Additionally, an example is included that provides students with insight into the construction and the behavior of the impulse function. These methods have been successfully taught to undergraduate engineering students to enhance their understanding of convolution and to facilitate their ability to evaluate convolution integrals.