HW1.4 Monil Goklani - Periodic and Non-periodic Functions ECE301Fall2008mboutin - Rhea

Discrete time periodic signal Example

Periodic Discrete Time Signal

Here the signal shown is $ x[n]= cos ((5*pi*n)/6) $

• For a signal to be periodic

$ cos(wn)= cosw(n+N) = cos(wn+wN) $

• i.e. wN must be an integer of 2*pi

$ wN = 2*pi*m $

Here the signal is periodic because $ {wN}/2*pi $ = {5*pi}/{6*2*pi} = 5/12 is a rational no.

Discrete Time Non-Periodic Signal

If the ratio of w/2*pi is an irrational no. then the signal would be classified as non-periodic