If
X(t)---->Time Delay of t - t0---->System----->Z(t) equation 1
X(t)---->System---->Time Delay of t - t0----->Y(t) equation 2
If eq.1 = eq.2 The System is Time-Variant.
Example of Time-InVariant System Y[t]= 10.X[t]
X[t]---->Time delay---->X[t-t0]----->System---->10(X[t-t0]) Result 1
X[t]---->System----->10(X[t])------>Time delay---->10(X[t-t0]) Result 2
As Reults 1 and 2 are equal. The System is Time-Invariant.
Example of a System which is not Time-Invariant Y(t)= X(t-1) - X(1-t)
X[t]---->Time delay---->X[t-t0]----->System---->X[t-t0-1]-X[1-t-t0] Result 1
X[t]---->System----->X[t-1]-X[1-t]------>Time delay---->X[t-t0-1]-X[1-t+t0] Result 2
As Results 1 and 2 are not Equal The system is not Time-Innvariant.
