EECE 301 Discussion 04 CT Convolution Examples

EECE 301 Discussion 04 CT Convolution Examples - EECE 301...

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Unformatted text preview: EECE 301 Signals & Systems Prof. Mark Fowler Discussion #4 C-T Convolution Examples C-T Convolution Examples Example 1: h ( t ) Zero ICs ) ( t f ) ( t y ) ( ) ( ) ( : : Find ) ( 2 ) ( ) ( ) ( ) ( : Given t h t f t y response state Zero t u e t t h t u e t f t t = + = = [ ] ) ( 2 ) ( ) ( ) ( ) ( ) ( t u e t t f t h t f t y t + = = Solution : First well use properties of convolution to break this down into sub-problems. By the distributive property we have: ) ( 2 ) ( ) ( ) ( ) ( t u e t f t t f t y t + = Call this convolution y 1 ( t ) call this h 1 ( t ) Use Property of Convolution with impulses ) ( ) ( ) ( 1 t y t f t y + = ) ( f 1 ) ( 1 h 2 ) ( f 1 ) ( t f 1 , = L t t L = , Flipped Flipped & Shifted Write as functions of : : ) ( ) ( product for cases Only two 1 t f h [ ] [ ] 1 2 1 2 2 2 ) ( 2 2 1 = = = = t t b t t e e e d e e d e e t y ) ( 1 < = t for e t y t RI: t < 0 ) ( 1 h ) ( t f t RII: t 0 ) ( 1 h ) ( t f t [ ] [ ] [ ] t t t t t t t e e e e e d e e t y...
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This note was uploaded on 02/29/2012 for the course EECE 301 taught by Professor Fowler during the Fall '08 term at Binghamton University.

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EECE 301 Discussion 04 CT Convolution Examples - EECE 301...

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