2025-L20 - ECE-2025 Spring-2004 Info: Web-CT, Lab, HW CHECK...

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ECE-2025 Spring-2004 Lecture 20 Fourier Transform Properties 29-Mar-04 3/27/2004 ECE-2025 Fall-03 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 3/27/2004 ECE-2025 Fall-03 jMc 3 Strategy for using the FT ± Develop a set of known Fourier transform pairs. ± Develop a set of “theorems” or properties of the Fourier transform. ± Develop skill in formulating the problem in either the time-domain or the frequency- domain, whichever leads to the simplest solution . 3/27/2004 ECE-2025 Fall-03 jMc 5 READING ASSIGNMENTS ± This Lecture: ± Chapter 11, Sects. 11-5 to 11-9 ± Tables in Section 11-9 ± Other Reading: ± Recitation: Chapter 11, Sects. 11-1 to 11-9 ± Next Lectures: Chapter 12 (Applications)
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3/27/2004 ECE-2025 Fall-03 jMc 6 LECTURE OBJECTIVES ± The Fourier transform ± More examples of Fourier transform pairs ± Basic properties of Fourier transforms ± Convolution property ± Multiplication property = dt e t x j X t j ω ) ( ) ( 3/27/2004 ECE-2025 Fall-03 jMc 7 Fourier Transform x ( t ) = 1 2 π X ( j ) e j t d −∞ Fourier Synthesis ( Inverse Transform) Time - domain Frequency - domain x ( t ) X ( j ) X ( j ) = x ( t ) −∞ e j t dt Fourier Analysis ( Forward Transform) 3/27/2004 ECE-2025 Fall-03 jMc 8 WHY use the Fourier transform? ± Manipulate the “Frequency Spectrum” ± Analog Communication Systems ± AM: Amplitude Modulation; FM ± What are the “ Building Blocks ” ?
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2025-L20 - ECE-2025 Spring-2004 Info: Web-CT, Lab, HW CHECK...

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