##
Relation to the *z* Transform

The Laplace transform is used to analyze *continuous-time*systems. Its discrete-time counterpart is the transform:

Note that the plane and plane are generally related by

*bandlimited to half the sampling rate*. As is well known, this condition is necessary to prevent

*aliasing*when sampling the continuous-time signal at the rate to produce , (see [84, Appendix G]).

**Next Section:**

Laplace Transform Theorems

**Previous Section:**

Analytic Continuation