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Unformatted text preview: 1 LINEAR TIME INVARIANCE 1 1 Linear Time Invariance 1. For each system below, determine if it is linear or non-linear, and determine if it is time-invariant or not time-invariant (adapted from Siebert 1986). (a) y ( t ) = u ( t + 1) The system is linear time-invariant; the output is just a time-advanced version of the input- it is noncausal! (b) y ( t ) = 1 /u ( t ) Nonlinear, time-invariant. Replace u ( t ) with αu ( t ) – this does not get us to αy ( t ), which would be required for linearity. (c) 3¨ y + ˙ y ( t ) − y ( t ) = u ( t ) Linear time-invariant; an unstable second-order system. We have to assume y (0) = 0, and that we are talking about delays only if u ( t ) = 0 for t < = 0. (d) y ( t ) = sin( t ) u ( t ) Linear time-varying. The coeﬃcient sin( t ) is a function of time, so if a given input trajectory is played with different starting times, the outputs will be different- unless the initial times are off by a integer multiple of 2 π ....
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- Spring '05