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ch2 lecture 2

# ch2 lecture 2 - EE 3120 Linear Systems Analysis Chapter 2...

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EE 3120 Linear Systems Analysis Chapter 2 Lecture 2 Time Invariance A system that has characteristics and properties that do not change with time is time-invariant. For a time-invariant, memoryless system the output is the same no matter the time the input is applied. A time-varying system ( ) 1 u t = ( ) sin( ) ( ) y t t u t = for at t A time-invariant system = ( ) sin ( ) y t u t ( ) 1 u t = for at t (0) sin(1) y = (1) sin(1) y = (0) sin(0)(1) 0 y = = (1) sin(1)(1) 0.84 y = = (2) sin(1) y = (2) sin(2)(1) .909 y = = For any memoryless system is linear iff it can be written It is also time-invariant iff is constant. ( ) ( ) ( ) y t a t u t = ( ) a t

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EE 3120 Linear Systems Analysis Chapter 2 Lecture 2 Time Invariance For a linear, time invariant (LTI) system system with memory, the initial state and input are the same, no matter what time they are applied, the output will always be the same. In other words – if the state and input are shifted by T, then the output is shifted by T. Properties of TI system are independent of time. An RLC circuit is TI if RLC are constant. The initial time is not critical for analysis of a TI system. We can set initial time = 0 and start to observe the system or apply input.
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ch2 lecture 2 - EE 3120 Linear Systems Analysis Chapter 2...

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