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.

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Questions/answers with a recent ECE grad

Ryne Rayburn