Periodic Functions
A great example for demonstrating periodic and non-periodic functions as well as differences between Discrete and Continuous Time is the sine function.
Continuous Time
Definition -The function x(t) is periodic if and only if there exists a number such that x(t+T) = x(t). The value of T is called the "period".
Using sin(t) as our example the smallest value for T is 2$ \pi $ so that sin(t+2$ \pi $)=sin(t), therefore this function is periodic in Continuous Time.
Discrete Time
Definition - The function x[n] is periodic if and only if there exists an integer N such that x[n+N] = x[n]. The value of N is called the "period".
There are no values which satisfy the requirements for N since 2$ \pi $ is not an integer, therefore the function is not periodic in Discrete Time.
