**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-t_{o}) → y(t-t_{o})

for discrete time

if x(t) → y(t), then x(t-t_{o}) → y(t-t_{o})

## How to check whether a system is time invariant or time varying

- Let y
_{1}(t) be the output corresponding to x_{1}(t). - Consider a second input x
_{2}(t) obtained by shifting x_{1}(t) i.e x_{2}(t) = x_{1}(t-t_{o}) and find the output corresponding to the input x_{2}(t). - From the step 1, find y
_{1}(t-t_{o}) and compare with y_{2}(t). - If y
_{2}(t) = y_{1}(t-t_{o}), then the system is time invariant; otherwise it is a time varying system.

Time-Varying & Time-Invariant Systems