2025-L21su10

# 2025-L21su10 - 1 1 ECE2025 Summer 2010 Lectures 21 Sampling...

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Unformatted text preview: 1 7/9/2010 1 ECE2025 Summer 2010 Lectures 21 Sampling and Reconstruction (Fourier View) Digital Filtering of Analog Signals, 2nd pass 26 Jul 10 7/9/2010 3 ANNOUNCEMENTS ¡ HW #9 due July 26-27 (last HW) ¡ Lab #10 July 28-29 (All in-lab) ¡ We’ve set aside time in lab for you to fill out the GaTech course surveys for ECE2025 7/9/2010 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 – look under quizzes) ¡ Tentative Review Session Sunday August 1, 8 pm, Klaus Room 2447. 7/9/2010 5 Table 1 (provided on final) 2 7/9/2010 6 Table 2 (provided on final) 7/9/2010 7 Tables 3 and 4 (also provided) 7/9/2010 8 LECTURE OBJECTIVES ¡ Sampling Theorem Revisited ¡ GENERAL: in the FREQUENCY DOMAIN ¡ Fourier transform of sampled signal ¡ Reconstruction from samples ¡ Effective frequency response ¡ Reading: Chap 12, Sections 12-1 and 12-3 ¡ Review of FT properties ¡ Convolution ÅÆ multiplication ¡ Frequency shifting 7/9/2010 9 Table of FT Properties x ( t − t d ) ⇔ e − j ω t d X ( j ω ) x ( t ) e j ω t ⇔ X ( j ( ω − ω )) Delay Property Frequency Shifting x ( at ) ⇔ 1 | a | X ( j ( ω a )) Scaling x ( t ) ∗ h ( t ) ⇔ H ( j ω ) X ( j ω ) 3 7/9/2010 10 Ideal C-to-D Converter • Mathematical Model for A-to-D x [ n ] = x ( nT s ) FOURIER TRANSFORM of x s (t) ???(t) ?...
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2025-L21su10 - 1 1 ECE2025 Summer 2010 Lectures 21 Sampling...

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