2025-L19 - ECE-2025 Spring-2004 Info: Web-CT, Lab, HW CHECK...

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ECE-2025 Spring-2004 Lecture 19 Introduction to the Fourier Transform 26-Mar-04 3/25/2004 ECE-2025 Spring-04 jMc 2 Info: Web-CT, Lab, HW ± CHECK YOUR GRADES !!! ± Web-CT is the OFFICIAL gradebook ± Quiz #3 will be 9-April (Friday) ± Coverage: HW #8, 9, and 10 ± Chapters 7, 9, 10, and 11 ± Review Session, 8-April, Thurs @ 7:30pm 3/25/2004 ECE-2025 Spring-04 jMc 3 THREE DOMAINS: ANALOG TIME-DOMAIN y ( t ) = h ( t ) * x ( t ) FREQ-DOMAIN R , L , C Laplace-TRANSFORM-DOMAIN POLYNOMIALS: H(s) X ( j ω ) = x ( t ) e j t dt −∞ Lecture 3/25/2004 ECE-2025 Spring-04 jMc 4 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
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3/25/2004 ECE-2025 Spring-04 jMc 5 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 ) ( ) ( 3/25/2004 ECE-2025 Spring-04 jMc 6 Everything = Sum of Sinusoids ± One Square Pulse = Sum of Sinusoids ± ??????????? ± Finite Length ± Not Periodic ± Limit of Square Wave as Period Æ infinity ± Intuitive Argument 3/25/2004 ECE-2025 Spring-04 jMc 7 Fourier Series: Periodic x(t) x ( t ) = x ( t + T 0 ) T 0 2 T 0 T 0 2 T 0 0 t x ( t ) = a k e j 0 kt k =−∞ a k = 1 T 0 x ( t ) e
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2025-L19 - ECE-2025 Spring-2004 Info: Web-CT, Lab, HW CHECK...

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