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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 (wont need to write any) Closed book, closed notes, except: One 8.5X11 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 6/3/2010 7 Harmonic Signal PERIOD/FREQUENCY of COMPLEX EXPONENTIAL: t f k j k k e a t x 2 ) ( = = ( ) 1 or 2 2 f T T f = = = 6/3/2010 8 k j k k N k k k e A X t kf A A t x = + + = = 1 ) 2 cos( ) ( k j k k k e A X a 2 1 2 1 = = Fourier Series Synthesis COMPLEX AMPLITUDE t f k j k k e a t x 2 ) ( = = 6/3/2010 9 STRATEGY: x(t) 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 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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