HW2.D Hetong Li ECE301Fall2008mboutin - Rhea

Definition

Time Invariance: A system is called "time invariance" if the system commutes the time delay by t0 for any t0

Time-invariant system

Example: for system: y(t)=3*x(t)

   x(t)->Time Delay by t0 in x(t)->y(t)=x(t-t0)->System->z(t)=3*y(t)=3*x(t-t0)
   x(t)->System->y(t)=3*x(t)->Time Delay by t0 in y(t)->z(t)=y(t-t0)=3*x(t-t0)
   Outputs are indetical so time invariant system

Time-variant system

Example: for system: y(t)=t*x(t)

   x(t)->Time Delay by t0 ->y(t)=t*x(t-t0)->System->z(t)=t*y(t)=t*x(t-t0)
   x(t)->System->y(t)=t*x(t)->Time Delay by t0 ->z(t)=y(t-t0)=(t-t0)*x(t-t0)
   Outputs are indetical so time invariant system