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| + | 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. | ||
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| + | == Example of Time Invariant == | ||
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| + | System --> sqrt[of signal] = Time invariant | ||
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| + | In other words, | ||
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| + | X(t) is input signal | ||
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| + | X(t) --> system --> y(t) = sqrt[X(t)] --> delay --> z(t) = sqrt[X(t - t0)] | ||
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| + | is equivalent to | ||
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| + | X(t) --> delay --> Y(t) = X(t - t0) --> system --> z(t) = sqrt[X(t - t0)] | ||
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| + | Therefore it is Time invariant. | ||
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| + | -Note: if i am wrong about this example, let me know. Thanks. | ||
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| + | == Example of not Time Invariant == | ||
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| + | x(t) --> system --> x(2t) | ||
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| + | X(t) --> system --> y(t) = x(2t) --> delay --> z(t) = x(2t - t0) | ||
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| + | X(t) --> delay --> y(t) = x(t - t0) --> system --> z(t) = x(2*(t-t0)) = x(2t - 2t0) | ||
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| + | These two outputs are not equal, so it is not a time invariant system. | ||
Latest revision as of 14:20, 11 September 2008
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.
