lecture21

lecture21 - EE313 Linear Systems and Signals Fall 2010...

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Unformatted text preview: EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Z-transforms 21 - 2 Z-transforms • For discrete-time systems, z-transforms play the same role of Laplace transforms do in continuous-time systems • As with the Laplace transform, we compute forward and inverse z-transforms by use of transforms pairs and properties [ ] ∑ ∞-∞ =- = n n z n h z H ) ( Bilateral Forward z-transform ∫ +- = R n dz z z H j n h 1 ) ( 2 1 ] [ π Bilateral Inverse z-transform 21 - 3 Region of Convergence • Region of the complex z- plane for which forward z-transform converges Im{ z } Re{ z } Entire plane Im{ z } Re{ z } Complement of a disk Im{ z } Re{ z } Disk Im{ z } Re{ z } Intersection of a disk and complement of a disk • Four possibilities ( z =0 is a special case and may or may not be included) 21 - 4 Z-transform Pairs • h [ n ] = δ [ n ] Region of convergence: entire z-plane • h [ n ] = δ [ n-1 ] Region of convergence: entire z-plane except z = h [ n-1] ⇔ z-1 H...
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lecture21 - EE313 Linear Systems and Signals Fall 2010...

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