ECE634S09_L17_BodePlots1 - ECE634 Signals and Systems II...

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ECE634 Signals and Systems II, Spring 2009 - Lecture 17, March 2 Daniel S. Brogan 1 4.8 Frequency Response of an LTIC System This section assumes that 0 s j j j σ ω ω ω = + = + = , 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 ( ) ( ) ( ) ( ) j H j H s H j H j e ω ω ω = = the response to an input at some frequency ω defined as ( ) ( ) cos x t A t ω θ = + will produce the output ( ) ( ) ( ) ( ) ( ) ( ) cos y t x t H j A H j t H j ω ω ω θ ω = = + + ∠ 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 ( ) 0.1 5 s H s s + = + Also, find the system response ( ) y t if the input ( ) x t is (a) ( ) cos 2 t (b) ( ) cos 10 50 t ° ( ) 0.1 5 j H j j ω ω ω + = + ( ) 2 2 2 2 2 2 0.1 0.01 5 25 H j ω ω ω ω ω + + = = + + ( ) 1 1 tan tan 0.1 5 H j ω ω ω =
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