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Unformatted text preview: 6.003: Signals and Systems Lecture 12 October 22, 2009 1 6.003: Signals and Systems CT Frequency Response and Bode Plots October 22, 2009 Midterm Examination #2 Wednesday, October 28, 7:309:30pm, Walker Memorial. No recitations on the day of the exam. Coverage: cumulative with more emphasis on recent material lectures 1–12 homeworks 1–7 Homework 7 includes practice problems for midterm 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 1hour exam; two hours to complete. Review sessions Monday 56pm and 89pm in 32044. Conflict? Contact [email protected] 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 splane s Response of an LTI system to an eternal cosine is an eternal cosine: same frequency, but scaled and shifted. H ( s ) cos( ω t )  H ( jω )  cos ( ω t + ⚢ H ( jω ) ) Frequency Response: H ( s )  s ← jω splane σ ω 5 − 5 5 − 5 H ( s ) = s − z 1 − 5 5 5  H ( jω )  − 5 5 π/ 2 − π/ 2 ⚢ H ( jω ) Frequency Response: H ( s )  s ← jω splane σ ω 5 − 5 5 − 5 H ( s ) = 9 s − p 1 − 5 5 5  H ( jω )  − 5 5 π/ 2 − π/ 2 ⚢ H ( jω ) Frequency Response: H ( s )  s ← jω splane σ ω 5 − 5 5 − 5 H ( s ) = 3 s − z 1 s − p 1 − 5 5 5  H ( jω )  − 5 5 π/ 2 − π/ 2 ⚢ H ( jω ) 6.003: Signals and Systems Lecture 12 October 22, 2009 2 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. σ ω 5 − 5 5 − 5 H ( jω ) = jω − z 1 − 5 5 5  H ( jω )  z 1 ω − 5 5 π/ 2 − π/ 2 ⚢ H ( jω ) Asymptotic Behavior: Isolated Zero Two asymptotes provide a good approxmation on loglog axes....
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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.
 Spring '11
 DennisM.Freeman
 Frequency

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