HW1.4 Hetong Li- Periodic and Non-Periodic Functions ECE301Fall2008mboutin - Rhea

Periodic Function

Periodic function of CT is $ y(t)=sin(t) $. Proof: $ y(t+T)= sin(t+T) $,where we take $ T=2*pi $.

      so $ sin(t+T)=sin(t+2*pi)=sin(t) $
      i.e $ y(t+T)=y(t) $.
      so it's periodic function.

Non-Periodic Function

Non-periodic function is $ y(t)=t $. Proof: assume y(t) is periodic, then there exists a non-zero T,that makes$ y(t+T)=y(t) $

      i.e. $ t+T=t $,so $ T=0 $,which violates the assumption.
      So $ y(t)=t $ is a non-periodic function