lecture23 - 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 Frequency Response of Discrete-Time Systems 23 - 2 Complex Exponentials • Two-sided 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 z-domain 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 • Real-valued 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 continuous-time sinusoid • Sample it every T s seconds ( see slide 7-6 ) • We show discrete-time sinusoid with • Resulting in • Discrete-time 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.

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lecture23 - EE313 Linear Systems and Signals Fall 2010...

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