Periodic functions
function
$ X[n]=\ {j^n} $
X[1]= j
X[2]= -1
X[3]= -j
X[4]= 1
X[5]= j
X[6]= -1
X[7]= -j
X[8]= 1
The function repeats its values after 4 and after every 4 values. So the given function is periodic with a period of 4.
Non-Periodic functions
function
$ X(t)=\ e^{jn} $
comparing it with e^{jwn} we get
w=1
i.e $ {w \over 2}= {1 \over 2 \pi} $
which is not rational. So the given function is not periodic.
