View source for HW1.4 Sourabh Ranka-Periodic and non-periodic functions with examples ECE301Fall2008mboutin - Rhea

==Periodic functions==

== function ==
<math>X[n]=\ {j^n}</math>

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 ==
<math>X(t)=\ e^{jn}</math>

comparing it with e^{jwn} we get 

w=1

i.e <math>{w \over 2}= {1 \over 2 \pi}</math> 

which is not rational. So the given function is not periodic.