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Unformatted text preview: Tom Penick [email protected] www.teicontrols.com/notes 4/4/98 THE Z-TRANSFORM Fundamentals of the Z-Transform The z-transform simplifies the analysis of linear time-invariant discrete-time (LTID) systems. It converts equations with integrals and derivatives into algebraic equations. The z-transform method of analyzing discrete-time systems is comparable to the Laplace transform method of analyzing continuous-time systems. THE UNILATERAL Z-TRANSFORM The unilateral z-transform 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 z-transform z is complex in general f [ k ] is a discrete-time signal THE INVERSE Z-TRANSFORM ∫- 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 z-transform z is complex in general f [ k ] is a discrete-time signal THE BILATERAL Z-TRANSFORM The bilateral z-transform is capable of analyzing both causal and non-causal systems.The bilateral z-transform is capable of analyzing both causal and non-causal systems....
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- Spring '11