Chapter 2 - Signal Properties

Periodicity

Continuous-time Signals

A periodic signal is a signal that repeats its behaviour over a certain period of time. A signal must exactly repeat itself over a fixed (non-zero) length in time, and must satisfy the definition:

\[ \exists\, T\in\mathbb{R}\setminus \{0\},\quad f(t) = f(t + T) \]

where the fundamental period \(T\) is the smallest positive value such that this is true.

A signal that does not satisfy this, for any \(T\) is called aperiodic or non-periodic.

Discrete-time Signals

For discrete-time signals, we have a similar definition:

\[ \exists\, N\in\mathbb{Z}\setminus \{0\},\quad f[n] = f[n + N] \]