2025-L06su09 - 5/28/2009 1 ECE2025 Summer 2009 Lectures 6...

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Unformatted text preview: 5/28/2009 1 ECE2025 Summer 2009 Lectures 6 Fourier Series Part 2 29 May 09 5/28/2009 3 ANNOUNCEMENTS HW 2 due June 1-2 June 3-4: Turn in Lab 2 Do lab 3 5/28/2009 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/ QA period: Klaus 2440, 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 5/28/2009 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) 5/28/2009 6 Review: Fourier Series Work with the Fourier Series Integral = ) / 2 ( 1 ) ( T dt e t x a t T k j T k 5/28/2009 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 = = = 5/28/2009 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 ) ( = = 5/28/2009 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 5/28/2009 10 Analysis is based on orthogonality of complex exponentials = = l l...
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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 Institute of Technology.

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2025-L06su09 - 5/28/2009 1 ECE2025 Summer 2009 Lectures 6...

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