Convolution Systems
Lecture slides: convolution-systems.pdf Download convolution-systems.pdf
Reading suggestion: KJA_pp71_101.pdf Download KJA_pp71_101.pdf
A convolution system is a special type of input-output system in which the output is given by the convolution of the input with the system's impulse response. In this lecture we discover that convolution systems are the systems that are linear, time-invariant, and causal. All of linear systems theory is really about convolution systems.
Apologies for writing off screen at the end. The only thing that you can't see are the dτs.
The main reason for using the Laplace transform for systems theory is that it turns convolutions into multiplications. This allows complex interconnected systems built out of convolution systems to be understood with tools from algebra.
Note there is a slight error at the end of the video when explaining the reordering of the integration. Try and correct the argument yourself!
The most common kinds of convolution systems are systems described by ordinary differential equations, and delays. Here we discuss these, as well as what to do about initial conditions.