Definition
The Z-transform is a mathematical tool used in automatic and signal processing, serving as the discrete counterpart of the Laplace transform in the continuous domain. Among other applications, we use it to compute digital filters with infinite impulse response and to discretely model dynamic systems. The Z-transform is a valuable tool for calculating the impulse response of a linear time-invariant system described by a finite difference equation.
We can derive the Z-transform from the Laplace transform.