This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 splane 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 splane 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 loglog 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 loglog 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 loglog plots of the frequencyresponse magnitudes of the following system functions:...
View Full
Document
 Summer '10
 staff

Click to edit the document details