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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.

## Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.