Contents
Time Invariant Systems
Worded Definitions
Time Invariant
A system is said to be time invariant if a time shift does not affect the output of the system. If x(t) is put through the system, then time shifted, the results should be identical to x(t) being time shifted, then put through the system.
Time Variant
A system is time variant if a time shift does affect the output of the system. In the same way as before, if x(t) is put through the system then time shifted, the results will be different than if x(t) is time shifted, then put through the system.
Example of a Time Invariant System
$ \,\!y(t)=x(t)sin(t) $
Step 1: The System
$ \,\!y(t)=2x(t)cos(t) $
Step 2: Time delay
$ \,\!z(t)=y(t-k)=2x(t-k)cos(t-k) $
Next, we do the time shift first, then the system:
$ \,\!y(t)=x(t-k) $ , now the system
$ \,\!z(t)=2y(t)cos(t)=2x(t-k)cos(t-k) $
These results are equal, so it is time invariant
