2025-L22su10

2025-L22su10 - 1 1 ECE2025 Summer 2010 Lecture 22 Digital...

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Unformatted text preview: 1 7/27/2010 1 ECE2025 Summer 2010 Lecture 22 Digital Filtering of Analog Signals, 3nd pass 28 Jul 10 7/27/2010 3 ANNOUNCEMENTS ¡ Lab #10 July 28-29 ¡ We’ve set aside time in lab for you to fill out the GaTech course surveys for ECE2025 7/27/2010 4 FINAL ¡ Monday, August 2: 11:30-14:20. ¡ Comprehensive, with extra emphasis on material not covered on first three quizzes . ¡ Closed book, closed notes, except: ¡ One 8.5”X11” crib sheet allowed, handwritten , OK to write on both side ¡ Formula sheet provided (Roughly book tables 8.1, 11.2, and 11.3) ¡ Review Session Friday 1:20 pm, this room. 7/27/2010 5 Table 1 2 7/27/2010 6 Table 2 7/27/2010 7 Tables 3 and 4 7/27/2010 8 LECTURE OBJECTIVES ¡ Effective frequency response ¡ Reading: Chap 12, Section 12-3.7 ¡ Review of FT properties ¡ Convolution ÅÆ multiplication ¡ Frequency shifting 7/27/2010 9 FOR FUN ¡ www.ratemyprofessors.com ¡ www.professorperformance.com ¡ www.profquotes.com 3 7/27/2010 10 Ideal C-to-D and D-to-C x [ n ] = x ( nT s ) x r ( t ) = x [ n ] sin π T s ( t − nT s ) π T s ( t − nT s ) n =−∞ ∞ ∑ Ideal Sampler Ideal band-limited interpolator X r ( j ω ) = H r ( j ω ) X s ( j ω ) X s ( j ω ) = 1 T s X ( j ( ω k =−∞ ∞ ∑ − k ω s )) 7/27/2010 11 DT Filtering of CT Signals D-to-C C-to-D x(t) y(t) y[n] x[n] H ( e j ˆ ω ) X ( j ω ) Y ( j ω ) X ( e j ˆ ω ) Y ( e j ˆ ω ) If no aliasing occurs in sampling x(t), then it follows that Y ( j ω ) = H eff ( j ω ) X ( j ω ) H eff ( j ω ) = H ( e j ω T s ) ω < 1 2 ω s ω > 1 2 ω s ⎧ ⎨ ⎩ UNDEFINED NOT LTI 7/27/2010 12 DT Filtering of a CT Signal Spectrum of Discrete-Time Signal Digital Filter Reconstruction Filter (Analog) ω ω ˆ ω ˆ ω Analog Input Analog Output 7/27/2010 13 EFFECTIVE Frequency Response ¡ Assume NO Aliasing, then ¡ ANALOG FREQ <--> DIGITAL FREQ ¡ So, we can plot: ¡ Scaled Freq. Axis ˆ ω =ω T s = ω f s H ( e j ω T s ) vs....
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This note was uploaded on 10/21/2010 for the course ECE 2025 taught by Professor Juang during the Summer '08 term at Georgia Tech.

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2025-L22su10 - 1 1 ECE2025 Summer 2010 Lecture 22 Digital...

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