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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 Ztransforms 21  2 Ztransforms • For discretetime systems, ztransforms play the same role of Laplace transforms do in continuoustime systems • As with the Laplace transform, we compute forward and inverse ztransforms by use of transforms pairs and properties [ ] ∑ ∞∞ = = n n z n h z H ) ( Bilateral Forward ztransform ∫ + = R n dz z z H j n h 1 ) ( 2 1 ] [ π Bilateral Inverse ztransform 21  3 Region of Convergence • Region of the complex z plane for which forward ztransform 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 Ztransform Pairs • h [ n ] = δ [ n ] Region of convergence: entire zplane • h [ n ] = δ [ n1 ] Region of convergence: entire zplane except z = h [ n1] ⇔ z1 H...
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 Spring '11
 EVANS
 Laplace, Inverse ZTransform, Finite impulse response

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