# 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 ] [ 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 ] = [ n ] Region of convergence: entire z-plane h [ n ] = [ n-1 ] Region of convergence: entire z-plane except z = 0 h [ n-1] z-1 H ( z ) [ ] [ ] 1...
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## This note was uploaded on 01/22/2012 for the course EE 312 taught by Professor Shafer during the Spring '08 term at University of Texas at Austin.

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

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