2025-L06su10

2025-L06su10 - 1 ECE2025 Summer 2010 Lectures 6 Fourier...

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Unformatted text preview: 6/3/2010 1 ECE2025 Summer 2010 Lectures 6 Fourier Series – Part 2 04 Jun 10 6/3/2010 3 ANNOUNCEMENTS ¡ HW 2 due June 7-8 ¡ June 9-10: ¡ Turn in Lab 2 ¡ Do lab 3 6/3/2010 4 FIRST QUIZ ¡ Quiz #1, in lecture, Friday, June 11 ¡ 10% of final grade ¡ You can use the full 1:20-2:30 time ¡ Review session/ QA period: June 10, Klaus 2441, 6-7 pm ¡ Coverage: ¡ HW #1 and #2 ¡ Lectures #1 through #5 (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” sheet allowed, handwritten , OK to write on both sides 6/3/2010 5 READING ASSIGNMENTS ¡ This Lecture: ¡ Fourier Series in Ch 3 Fourier Series in Ch 3 ¡ Notation: a k for Fourier Series ¡ Other Reading: ¡ Next Topic: Sampling (not on Q1 either) 6/3/2010 6 Review: Fourier Series ¡ Work with the Fourier Series Integral ∫ − = ) / 2 ( 1 ) ( T dt e t x a t T k j T k π 6/3/2010 7 Harmonic Signal PERIOD/FREQUENCY of COMPLEX EXPONENTIAL: t f k j k k e a t x 2 ) ( π ∑ ∞ −∞ = = ( ) 1 or 2 2 f T T f = = = π ω π 6/3/2010 8 k j k k N k k k e A X t kf A A t x ϕ ϕ π = + + = ∑ = 1 ) 2 cos( ) ( k j k k k e A X a ϕ 2 1 2 1 = = Fourier Series Synthesis COMPLEX AMPLITUDE t f k j k k e a t x 2 ) ( π ∑ ∞ −∞ = = 6/3/2010 9 STRATEGY: x(t) Æ a k ¡ ANALYSIS ¡ Get representation from the signal ¡ Works for PERIODIC PERIODIC Signals ¡ Fourier Series ¡ Answer is: an INTEGRAL over one period ∫ − = ) ( 1 T dt e t x a t k j T k ω 6/3/2010 10 Analysis is based on orthogonality of complex exponentials ⎪ ⎩ ⎪ ⎨ ⎧ = ≠ = ∫ − l l l k k dt e e T T kt T j t T j 1...
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2025-L06su10 - 1 ECE2025 Summer 2010 Lectures 6 Fourier...

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