A time invariant system is a system for which when a signal passes through a system and then is time shifted, it is equal to when the signal is time shifted and then passed through the system.
Example of Time Invariant
System --> sqrt[of signal] = Time invariant
In other words,
X(t) is input signal
X(t) --> system --> y(t) = sqrt[X(t)] --> delay --> z(t) = sqrt[X(t - t0)]
is equivalent to
X(t) --> delay --> Y(t) = X(t - t0) --> system --> z(t) = sqrt[X(t - t0)]
Therefore it is Time invariant.
-Note: if i am wrong about this example, let me know. Thanks.
Example of not Time Invariant
x(t) --> system --> x(2t)
X(t) --> system --> y(t) = x(2t) --> delay --> z(t) = x(2t - t0)
X(t) --> delay --> y(t) = x(t - t0) --> system --> z(t) = x(2*(t-t0)) = x(2t - 2t0)
These two outputs are not equal, so it is not a time invariant system.
