Freq_anal_text

Freq_anal_text - Chap 5. Frequency Domain Analysis of...

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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 ) ( ) ( ) ( H X Y = where ) ( ) ( X t x ) ( ) ( Y t y ) ( ) ( H t h H( ) 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 ) ( ) ( = = + 1.2 Response to sinusoids ) cos( ) ( + = t t x 1.3 Response to periodic input = = k t jk k e c t x ) ( IFT LTIs can be viewed as Frequency selective filters: ( ) y k k c H k c = ( ) 1, Amplify the frequency component H k > ( ) 1 , A t t e n u a t e H k < ( ) 0, Eliminate or block H k = 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 This is the frequency response of a first-order system that is used to...
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Freq_anal_text - Chap 5. Frequency Domain Analysis of...

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