# Useful Definitions for ECE301: signals and systems

**Periodic CT Signal:**

- A CT signal $ x(t)\ $ is called periodic if there exists $ T>0\ $ period such that $ x(t+T)=x(t)\ $, for all values of t. The fundamental period is the smallest period of all periods of a signal (denoted by $ T_0\ $).

In Mathspeak:

- $ x(t) periodic \iff \exists T>0 \ni x(t+T)=x(t), \forall t \in \mathbb{R} $

**Periodic DT Signal:**

- A DT signal $ x[n]\ $ is called periodic if there exists $ N>0\ $ period such that $ x[n+N]=x[n]\ $, for all values of n. the fundamental period is the smallest period of all periods of a signal (denoted by $ N_0\ $).

In Mathspeak:

- $ x[n] periodic \iff \exists N>0 \ni x[n+N]=x[n], \forall n \in \mathbb{N} $

Comment:

- The difference between CT and DT:

Note that the period N must be an integer in DT, but that the period T in CT can be any positive real number.

-Mimi (Wed, 26 Sep 2007 16:29:43)