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== Example of not Time Invariant system == | == Example of not Time Invariant system == | ||
| − | + | y(t) = t*x(t) | |
| + | |||
| + | x(t) = 2t | ||
| + | |||
| + | x(t) through y(t) yields y(t) = t*2t | ||
| + | |||
| + | y(t-4) = (t-4)*(t-4)*t | ||
| + | |||
| + | x(t-4) through y(t) yields y(t-4) = t*2*(t-4) | ||
| + | |||
| + | these are not the same so this system is not time invariant | ||
Latest revision as of 15:43, 12 September 2008
Time Invariance
A system is time invariant if x(t) passed through the system yeilds y(t) and x(t-T) for any value of T yeilds y(t-T). Time shifting before you put something through the system and after you put it through the system gives you the same results.
Example of Time Invariance
y(t) = x(t)/4
x(t) = cos(t)+sin(t)
x(t) through y(t) yields y(t) = cos(t)/4 + sin(t)/4
x(t-4) through y(t) yields y(t-4) = cos(t-4)/4 + sin(t-4)/4
the signal is time invariant
Example of not Time Invariant system
y(t) = t*x(t)
x(t) = 2t
x(t) through y(t) yields y(t) = t*2t
y(t-4) = (t-4)*(t-4)*t
x(t-4) through y(t) yields y(t-4) = t*2*(t-4)
these are not the same so this system is not time invariant
