HW1.4 Paul Scheffler - Periodic and Non-Periodic Functions ECE301Fall2008mboutin - Rhea

Periodic Function

$ y(x)=x+3 $

Proof: Assuming that y(x) is periodic, then there must be a non-zero integer T,that makes y(x+T)=y(x).
       y(x+T)=x+3 with any T that is a multiple of 3 will work.
       Therefore y(x)=t+3 is aperiodic function.

Non-Periodic Functions

$ y(x)=1 $

Proof: Assuming that y(x) is periodic, then there must be a non-zero integer T,that makes y(x+T)=y(x).
       y(x+T)=1 For all T except 0.
       Therefore y(x)=1 is a non-periodic function.