Time-Invariant System
The system is time invariant if the behaviour and characteristic of the system are fixed over time. In other words, a system is said to be time invariant if a time shift in the input signal causes an identical time shift in the output signal.
It means that
for continuous time
if x(t) → y(t), then x(t-to) → y(t-to)
for discrete time
if x(t) → y(t), then x(t-to) → y(t-to)
How to check whether a system is time invariant or time varying
- Let y1(t) be the output corresponding to x1(t).
- Consider a second input x2(t) obtained by shifting x1(t) i.e x2(t) = x1(t-to) and find the output corresponding to the input x2(t).
- From the step 1, find y1(t-to) and compare with y2(t).
- If y2(t) = y1(t-to), then the system is time invariant; otherwise it is a time varying system.
