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Unformatted text preview: Chap 5. Frequency Domain Analysis of Linear Systems 1. Frequency response of LTI Systems. Considering an LTI system with input x(t), output y(t) and impulse response h(t) → ) ( t x ) ( t h ) ( ) ( ) ( t h t x t y ∗ = → From the convolution property of FT ) ( ) ( ) ( ω ω ω H X Y ∗ = where ) ( ) ( ω X t x ↔ ) ( ) ( ω Y t y ↔ ) ( ) ( ω H t h ↔ H( ω ) is the frequency response function of the LT1 system. It completely characterizes the LT1 system 1.1 Response to t j j t j e e e t x ) ( ) ( ω θ θ ω = = + 1.2 Response to sinusoids ) cos( ) ( θ ω + = t t x 1.3 Response to periodic input ∑ ∞ −∞ = = k t jk k e c t x ) ( ω IFT LTIs can be viewed as Frequency selective filters: ( ) y k k c H k c ω = ( ) 1, Amplify the frequency component H k ω > ( ) 1 , A t t e n u a t e H k ω < ( ) 0, Eliminate or block H k ω = Filter example: 1. RC circuit 1 1 1 1 ) ( ) ( 1 ) ( 1 + = + = = − RC j RC j RC H t u e RC t h t RC ω ω ω This is the frequency response of a first-order system that is used to...
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This note was uploaded on 10/15/2010 for the course BIM BIM108 taught by Professor Qiu during the Winter '09 term at UC Davis.
- Winter '09