2025-L22su10

2025-L22su10 - 1 7/27/2010 1 ECE2025 Summer 2010 Lecture 22...

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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 Weve 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 8.5X11 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 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 T s ( t nT s ) T s ( t nT s ) n = Ideal Sampler Ideal band-limited interpolator X r ( j ) = H r ( j ) X s ( j ) X s ( j ) = 1 T s X ( j ( k = k 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 ) X ( j ) Y ( j ) X ( e j ) Y ( e j ) If no aliasing occurs in sampling x(t), then it follows that Y ( j ) = H eff ( j ) X ( j ) H eff ( j ) = H ( e j T s ) < 1 2 s > 1 2 s UNDEFINED NOT LTI 7/27/2010 12 DT Filtering of a CT Signal Spectrum of Discrete-Time Signal Digital Filter Reconstruction Filter (Analog) 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 = T s = f s H ( e j T s ) vs....
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2025-L22su10 - 1 7/27/2010 1 ECE2025 Summer 2010 Lecture 22...

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