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Unformatted text preview: Tom Penick [email protected] www.teicontrols.com/notes 4/4/98 THE ZTRANSFORM Fundamentals of the ZTransform The ztransform simplifies the analysis of linear timeinvariant discretetime (LTID) systems. It converts equations with integrals and derivatives into algebraic equations. The ztransform method of analyzing discretetime systems is comparable to the Laplace transform method of analyzing continuoustime systems. THE UNILATERAL ZTRANSFORM The unilateral ztransform is capable of analyzing only causal systems with causal inputs (signals starting at k = 0). ∑ ∞ = ≡ ] [ ] [ k k z k f z F where: F [ z ] is the ztransform z is complex in general f [ k ] is a discretetime signal THE INVERSE ZTRANSFORM ∫ π = dz z z F j k f k 1 ] [ 2 1 ] [ where: ∫ indicates integration around a circular path in the complex plane centered at the origin F [ z ] is the ztransform z is complex in general f [ k ] is a discretetime signal THE BILATERAL ZTRANSFORM The bilateral ztransform is capable of analyzing both causal and noncausal systems.The bilateral ztransform is capable of analyzing both causal and noncausal systems....
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 Spring '11
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