Can we say that a Linear Constant Coefficient Difference Equation can always represent a Linear Shift Invarient system ? Are there any conditions which need to be satisfied additionally by these kind of equations to be able to do that?
Can Linear Constant coefficient Difference Equations always represent an LTI system?
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2 Answers
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The above link is a pdf that has the answer to your question.
It is not necessary that a linear constant coefficient difference equation must represent an LTI system. It will represent an LTI system if and only if the solution satisfies the initial rest condition, namely if $x[n] = 0$ for $n
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0@svenkatr Cant get you. Necessary for what ? – 2012-08-27
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WHat about final rest condition? (i.e if x(t) = 0, for t > t0 then y(t) is also 0 for t > t0 ) whether now the differential equation satisfies LSI or not?
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0Thank you.Initial rest condition is not necessary condition for linearity. But it is essential for Time invariance to satisfy.For linearity alone, zero initial condition like y(1) = 0 (which is not initial rest condition) is enough. – 2013-05-25