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ECE634 Signals and Systems II, Spring 2009 - Lecture 17, March 2 Daniel S. Brogan 14.8 Frequency Response of an LTIC System •This section assumes that 0sjjjσωωω=+=+=, i.e. we are only concerned with the steady-state component of the response. Since the frequency response of an LTIC system can be defined as ( )()()()jHjHsHjHjeωωω∠==the response to an input at some frequency ωdefined as ( )()cosx tAtωθ=+will produce the output ( )( )()()()()cosy tx t HjA HjtHjωωωθω==++ ∠Note that the magnitude and phase of the output may vary with frequency. •Example 4.23 (Lathi p.424) Find the frequency response (amplitude and phase response) of a system whose transfer function is ( )0.15sHss+=+Also, find the system response ( )y tif the input ( )x tis (a) ()cos 2t(b) ()cos 1050t−°()0.15jHjjωωω+=+()2222220.10.01525Hjωωωωω++==++()11tantan0.15Hjωωω−−⎛⎞⎛⎞∠=−⎜⎟⎜⎟⎝⎠⎝⎠
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