Periodic versus non-periodic functions (hw1, ECE301)

Read the instructor's comments here.

Definiton: A DT signal x[n] is called periodic if there exists an integer N such that x[n+N]=x[n] for all n.

Example

x[n]=j^n, is periodical with fundemental period N0=4. x[1]=j x[5]=j x[2]=-1 x[6]=-1 x[3]=-j x[7]=-j x[4]=1 x[8]=1

Example for a CT singnal

Non Periodic Functions

DT Example: sin[n] is not a periodic DT signal because we need a value on N such that sin(n+N)=sin(n) for all n. Every possible multiple of N is is not an integer. Thus it is not periodic.

CT