The z-transform: Basics and Applications

This lecture covers the basics of the z-transform, including its definition as a power series and its application to linear, time-invariant systems. It explains how to compute frequency and impulse responses, as well as the transfer function. The lecture also delves into polynomial multiplication, convolution, and the convergence of the z-transform. Practical examples are provided to illustrate the concepts, such as applying the z-transform to constant-coefficient difference equations and analyzing rational transfer functions. Additionally, the lecture revisits the leaky integrator system and discusses the relationship between the impulse response and the transfer function.