Properties of the $z$-Transform

The $z$-transform has several important properties. In this lesson you will learn the most commonly used properties of the $z$-transform in the analysis of signals and systems. In particular, the convolution-multiplication property introduces the characterization of linear time-invariant systems using the $z$-transform of the impulse response, which is called the system function. The time-shift property allows us to easily find the system function for a system described by a linear constant coefficient difference equation. The system function is the basis for using $z$-transforms to study systems, the topic of the following six lessons.