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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 Frequency Response of DiscreteTime Systems 23  2 Complex Exponentials • Twosided complex exponential z n when input into LTI systems Output will be same complex exponential weighted by H ( z ) Provided that z is in region of convergence for H ( z ) • When we specialize the zdomain to frequency domain, the magnitude of H ( z ) will control which frequencies are attenuated or passed [ ] [ ] [ ] [ ] [ ] ) ( ] [ z H z z m h z z m h z n h n x n h n y n m m n m m n n = = = = = ∑ ∑ ∞∞ = ∞∞ = 23  3 Frequency Response for LTI Systems • Continuous time • Discrete time • Realvalued impulse response: H ( e j ω ) = H* ( e j ω ) Input Output ( 29 ( 29 ( 29 ( 29 ( 29 ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ) ( ) ( cos 2 j j k j e H j j k j e H j j e H ω k e H e e e H e e e H j j ∠ + = + = ∠ ∠ ) cos( 2 k e e k j k j ϖ ϖ ϖ = + ] [ k h k j e ϖ ( 29 k j j e e H ϖ ϖ ( 29 k cos ϖ ( 29 ( 29 ( 29 ϖ ϖ ϖ cos j j e H k e H ∠ + ) ( t h t j e Ω ( 29 t j e j H Ω Ω ( 29 ( 29 ( 29 Ω ∠ + Ω Ω j H t j H cos ( 29 t cos Ω ( 29 ( 29 ( 29 ( 29 k j j k j j k j j k j j e e H e e H e e H e e H * ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ + = + 23  4 Response to Sampled Sinusoids • Start with a continuoustime sinusoid • Sample it every T s seconds ( see slide 76 ) • We show discretetime sinusoid with • Resulting in • Discretetime frequency is equal to continuous time frequency multiplied by sampling period...
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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.
 Spring '08
 Shafer
 Frequency

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