Periodic versus non-periodic functions (hw1, ECE301)

Read the instructor's comments here.

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.