Peridic and Non Periodic Signals
Defination :
-if x(t)=x(t+T) for all values of t ,for some T not equal to zero,then x(t) is periodic with period T.
-if x(n)=x(n+N) for all values of n ,some integer N ,then x(n) is periodic with period N.
Example of a periodic signal
Q) Is x[n]=j^n periodic ?
Ans)
fundamental period of signal N=4
x[1] = j x[2] = -1 x[3] = -j x[4] = 1 x[5] = j x[6] = -1 x[7] = -j x[8] = 1
period =4,8,16 ,all mulitples of 4.
Therefore it is a periodic signal
Example of a non periodic signal.
q) Is cos(n) a periodic signal ?
- we want a integer N such that
cos (n+N) = cos (n) for all n
N is a multiple of 2*pi but since no integer multiple of 2*pi is an integer Therefore cos (n) is not periodic.
