Signals and Systems Concepts

We must first introduce some concepts related to signals and systems.

Definitions

Signals is either a function defined over a continuous domain or a sequence.

System is a transformer that takes a signal and transforms it to another signal.

Continuity and discreteness

If a signal is a function defined over a continuous domain, because the variable in it is continuous, it is called continuous signal. We usually just note it as a function $x(t)$.

discrete signal is a sequence defined only on certain points (usually at integer values). We usually note it as a sequence $x[n]$.

If a system takes a continuous signal and transforms it to a continuous signal, it is called continuous system.

If a system takes a discrete signal and transforms it to a discrete signal, it is called discrete system.

If a system takes a continuous signal and transforms it to a discrete signal, it is called a sampling system.

If a system takes a discrete signal and transforms it to a continuous signal, it is called a interpolation system.