SPFirst-L22

SPFirst-L22 - 3/27/2004 © 2003, JH McClellan & RW...

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Unformatted text preview: 3/27/2004 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 22 Introduction to the Fourier Transform 3/27/2004 © 2003, JH McClellan & RW Schafer 3 READING ASSIGNMENTS ¡ This Lecture: ¡ Chapter 11, Sects. 11-1 to 11-4 ¡ Other Reading: ¡ Recitation: Ch. 10 ¡ And Chapter 11, Sects. 11-1 to 11-4 ¡ Next Lecture: Chapter 11, Sects. 11-5, 11-6 3/27/2004 © 2003, JH McClellan & RW Schafer 4 LECTURE OBJECTIVES ¡ Review ¡ Frequency Response ¡ Fourier Series ¡ Definition of Fourier transform Relation to Fourier Series ¡ Examples of Fourier transform pairs ∫ ∞ ∞ − − = dt e t x j X t j ω ω ) ( ) ( 3/27/2004 © 2003, JH McClellan & RW Schafer 5 Everything = Sum of Sinusoids ¡ One Square Pulse = Sum of Sinusoids ¡ ??????????? ¡ Finite Length ¡ Not Periodic ¡ Limit of Square Wave as Period Æ infinity ¡ Intuitive Argument 3/27/2004 © 2003, JH McClellan & RW Schafer 6 Fourier Series: Periodic x(t) x ( t ) = x ( t + T ) T − 2 T − T 2 T t x ( t ) = a k e j ω k t k =−∞ ∞ ∑ a k = 1 T x ( t ) e − j ω kt dt − T / 2 T / 2 ∫ Fundamental Freq. ω = 2 π / T = 2 π f Fourier Synthesis Fourier Analysis 3/27/2004 © 2003, JH McClellan & RW Schafer 7 Square Wave Signal a k = e − j ω kt − j ω kT − T /4 T / 4 = e − j π k...
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This note was uploaded on 03/03/2010 for the course EE 48976 taught by Professor Nayak during the Spring '10 term at USC.

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SPFirst-L22 - 3/27/2004 © 2003, JH McClellan & RW...

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