The Z-Transform

The $z$-transform is an important signal-processing tool for analyzing the interaction between signals and systems. A significant advantage of the $z$-transform over the discrete-time Fourier transform is that the $z$-transform exists for many signals that do not have a discrete-time Fourier transform. Thus, it is a more general analysis tool. In this series of 13 lessons you will learn how to work with the $z$-transform and use it to characterize signal processing systems. You will learn how the poles and zeros of a system tell us whether the system can be both stable and causal, and whether it has a stable and causal inverse system. You will also learn how the pole and zero locations of a system give us insight into the nature of its frequency and impulse response. The insights gained with the $z$-transform are particularly useful for designing frequency-selective filters.