lec12 - 6.003: Signals and Systems CT Frequency Response...

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Unformatted text preview: 6.003: Signals and Systems CT Frequency Response and Bode Plots October 22, 2009 Mid-term Examination #2 Wednesday, October 28, 7:30-9:30pm, Walker Memorial. No recitations on the day of the exam. Coverage: cumulative with more emphasis on recent material lectures 112 homeworks 17 Homework 7 includes practice problems for mid-term 2. It will not collected or graded. Solutions will be posted. Closed book: 2 pages of notes ( 8 1 2 11 inches; front and back). Designed as 1-hour exam; two hours to complete. Review sessions Monday 5-6pm and 8-9pm in 32-044. Conflict? Contact freeman@mit.edu by Friday, October 23, 5pm. Last Time Complex exponentials are eigenfunctions of LTI systems. H ( s ) e s t H ( s ) e s t H ( s ) can be determined graphically using vectorial analysis. H ( s ) = K ( s z )( s z 1 )( s z 2 ) ( s p )( s p 1 )( s p 2 ) z z s z s s-plane s Response of an LTI system to an eternal cosine is an eternal cosine: same frequency, but scaled and shifted. H ( s ) cos( t ) | H ( j ) | cos ( t + H ( j ) ) Frequency Response: H ( s ) | s j s-plane 5 5 5 5 H ( s ) = s z 1 5 5 5 | H ( j ) | 5 5 / 2 / 2 H ( j ) Frequency Response: H ( s ) | s j s-plane 5 5 5 5 H ( s ) = 9 s p 1 5 5 5 | H ( j ) | 5 5 / 2 / 2 H ( j ) Frequency Response: H ( s ) | s j s-plane 5 5 5 5 H ( s ) = 3 s z 1 s p 1 5 5 5 | H ( j ) | 5 5 / 2 / 2 H ( j ) Poles and Zeros Thinking about systems as collections of poles and zeros is an im- portant design concept. simple: just a few numbers characterize entire system powerful: complete information about frequency response Today: poles, zeros, frequency responses, and Bode plots. Asymptotic Behavior: Isolated Zero The magnitude response is simple at low and high frequencies. 5 5 5 5 H ( j ) = j z 1 5 5 5 | H ( j ) | 5 5 / 2 / 2 H ( j ) Asymptotic Behavior: Isolated Zero The magnitude response is simple at low and high frequencies. 5 5 5 5 H ( j ) = j z 1 5 5 5 | H ( j ) | z 1 5 5 / 2 / 2 H ( j ) Asymptotic Behavior: Isolated Zero The magnitude response is simple at low and high frequencies. 5 5 5 5 H ( j ) = j z 1 5 5 5 | H ( j ) | z 1 5 5 / 2 / 2 H ( j ) Asymptotic Behavior: Isolated Zero Two asymptotes provide a good approxmation on log-log axes. H ( s ) = s z 1 5 5 5 | H ( j ) | 2 1 1 2 2 1 log z 1 1 log | H ( j ) | z 1 lim | H ( j ) | = z 1 lim | H ( j ) | = Asymptotic Behavior: Isolated Pole The magnitude response is simple at low and high frequencies....
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This note was uploaded on 08/24/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.

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lec12 - 6.003: Signals and Systems CT Frequency Response...

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