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| − | '''X(t)'''---->Time Delay of'''t-t0'''---->System----->Z(t) equation 1 | + | '''X(t)'''---->Time Delay of '''t - t0'''---->System----->Z(t) equation 1 |
| − | '''X(t)'''---->System---->Time Delay of'''t-t0'''----->Y(t) equation 2 | + | '''X(t)'''---->System---->Time Delay of '''t - t0'''----->Y(t) equation 2 |
If eq.1 = eq.2 The System is Time-Variant. | If eq.1 = eq.2 The System is Time-Variant. | ||
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| + | '''Example of Time-InVariant System''' Y[t]= 10.X[t] | ||
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| + | X[t]---->Time delay---->X[t-t0]----->System---->10(X[t-t0]) Result 1 | ||
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| + | X[t]---->System----->10(X[t])------>Time delay---->10(X[t-t0]) Result 2 | ||
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| + | As Reults 1 and 2 are equal. '''The System is Time-Invariant'''. | ||
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| + | '''Example of a System which is not Time-Invariant''' Y(t)= X(t-1) - X(1-t) | ||
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| + | X[t]---->Time delay---->X[t-t0]----->System---->X[t-t0-1]-X[1-t-t0] Result 1 | ||
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| + | X[t]---->System----->X[t-1]-X[1-t]------>Time delay---->X[t-t0-1]-X[1-t+t0] Result 2 | ||
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| + | As Results 1 and 2 are not Equal The system is '''not Time-Innvariant'''. | ||
Latest revision as of 13:24, 12 September 2008
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.
