MIT6_003S10_lec10_handout

MIT6_003S10_lec10_handout - 6.003: Signals and Systems...

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Unformatted text preview: 6.003: Signals and Systems Lecture 10 March 9, 2010 6.003: Signals and Systems CT Frequency Response and Bode Plots March 9, 2010 Frequency Response: H ( s ) | s j | H ( j ) | H ( s ) = 3 s z 1 5 s p 1 5 s-plane 5 5 H ( j ) 5 / 2 5 5 5 5 / 2 Asymptotic Behavior: Isolated Zero The magnitude response is simple at low and high frequencies. | H ( j ) | H ( j ) = j z 1 5 5 z 1 5 5 H ( j ) 5 5 / 2 5 5 5 / 2 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 ) ) 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 Two asymptotes provide a good approxmation on log-log axes. H ( s ) = s z 1 log | H ( j ) | | H ( j ) | 2 z 1 5 1 1 log 5 5 2 1 1 2 z 1 lim | H ( j ) | = z 1 lim | H ( j ) | = 1 6.003: Signals and Systems Lecture 10 March 9, 2010 Asymptotic Behavior: Isolated Pole Asymptotic Behavior: Isolated Pole Two asymptotes provide a good approxmation on log-log axes. The magnitude response is simple at low and high frequencies. 9 9 9 | H ( j ) | H ( s ) = s p 1 H ( s ) = 5 s p 1 9 log | H ( j ) | 9 /p 1 5 p 1 | H ( j ) | 5 5 5 1 1 H ( j ) 2 5 / 2 5 log 5 5 2 1 1 2 p 1 5 5 9 lim | H ( j ) | = p 1 5 / 2 9 lim | H ( j ) | = Check Yourself Asymptotic Behavior of More Complicated Systems Compare log-log plots of the frequency-response magnitudes of the following system functions:...
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MIT6_003S10_lec10_handout - 6.003: Signals and Systems...

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