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== Examples of Time Invariant Systems == | == Examples of Time Invariant Systems == | ||
| + | y(t)=x(t)-2 | ||
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| + | x(t)-->|System|-{y(t)=x(t)-2}->|Time Shift by b|--> z(t)= x(t-b)-2 | ||
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| + | x(t)-->|Time Shift by b|-{w(t)=x(t-b)}->|System|--> z(t)= x(t-b)-2 | ||
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| + | Since y(t)=x(t)-2 results in the same output, it is called time invariant. | ||
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| + | y(t)=x(2t) | ||
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| + | x(t)-->|System|-{y(t)=x(2t)}->|Time Shift by b|--> z(t)= x(2t-2b) | ||
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| + | x(t)-->|Time Shift by b|-{w(t)=x(2t-b)}->|System|--> z(t)= x(2t-b) | ||
| + | Since y(t)=x(2t) does not yield the same results for by series, it is called time variant. | ||
Latest revision as of 10:13, 11 September 2008
Time Invariant Systems
A system is time invariant if you can time shift the input by one amount and then put the input through the system and get an out if you can also put the input through the system and then time shift using the same value and have identical outputs.
Examples of Time Invariant Systems
y(t)=x(t)-2
x(t)-->|System|-{y(t)=x(t)-2}->|Time Shift by b|--> z(t)= x(t-b)-2
x(t)-->|Time Shift by b|-{w(t)=x(t-b)}->|System|--> z(t)= x(t-b)-2
Since y(t)=x(t)-2 results in the same output, it is called time invariant.
y(t)=x(2t)
x(t)-->|System|-{y(t)=x(2t)}->|Time Shift by b|--> z(t)= x(2t-2b)
x(t)-->|Time Shift by b|-{w(t)=x(2t-b)}->|System|--> z(t)= x(2t-b)
Since y(t)=x(2t) does not yield the same results for by series, it is called time variant.
