2025-L07su09

2025-L07su09 - 1 ECE2025 Summer 2009 Lecture 7 Sampling&...

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Unformatted text preview: 5/29/2009 1 ECE2025 Summer 2009 Lecture 7 Sampling & Aliasing 01 Jun 09 5/29/2009 3 ANNOUNCEMENTS ¡ HW 2 due 1-2 June ¡ 3-4 June: ¡ Turn in Lab 2 ¡ Do lab 3 (Bring Headphones) ¡ HW 3 due 8-9 June ¡ 10-11 June: ¡ Turn in Lab 3 ¡ Do Lab 4 5/29/2009 4 FIRST QUIZ ¡ Quiz #1, in lecture, Friday, June 5 ¡ 10% of final grade ¡ You can use the full 1:20-2:30 time ¡ Review session June 4, 6-7 pm in Lab. ¡ Coverage: ¡ HW #1 and #2 ¡ Lectures #1 through #5 (but no Fourier series) ¡ Might have to read some MATLAB code (won’t need to write any) ¡ Closed book, closed notes, except: ¡ One 8.5”X11” crib sheet allowed, handwritten , OK to write on both sides 5/29/2009 5 Fourier Series: Final Thoughts ∫ − = ) / 2 ( 1 ) ( T t k T j T k dt e t x a π real is ) ( when * t x a a k k = − t f k j N N k k e a t x 2 ) ( π ∑ − = = ∫ + + − = δ δ π ) 2 ( 1 ) ( T t k f j T k dt e t x a 5/29/2009 6 Fourier Series Properties If x(t)=x(-t) (even symmetry), only cosines are used. The coefficients are pure real. ( a k = a-k and a k = a *-k ) If x(t)=-x(-t) (odd symmetry), only sines are used. The coefficients are pure imaginary. ( a k = -a-k and a k = a *-k ) If x(t) is delayed: y(t)=x(t-d), the coefficients have the same magnitude, but have a phase of - dk ω 0 added. If the FS coefficients of x(t) are a k , then the FS coefficients of y(t) will be exp(-jk ω d)a k . A delay by ½ period converts the coeffcients to (-1) k a k ....
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This note was uploaded on 01/24/2010 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Tech.

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2025-L07su09 - 1 ECE2025 Summer 2009 Lecture 7 Sampling&...

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