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.

Alumni Liaison

BSEE 2004, current Ph.D. student researching signal and image processing.

Landis Huffman