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Unformatted text preview: 1 1 Summary of Lecture #20 10/08/2010 Convolution integral Flip, shift, multiply and integrate Key properties of convolution integrals Evaluate convolution integrals- Examples Properties of Delta function, (t), a review Convolution with Delta function Graphical convolution- examples - - - = - = = d ) t ( h ) ( f d ) ( h ) t ( f ) t ( h ) t ( f ) t ( y 2 h(t) (t) h(t) h(t) (t-t 0) h(t-t 0) h(t) a (t-t 1) a h(t-t 1) t 1 >0 h(t) b (t-t 2) t 2<0 b h(t-t 2) h(t) h(t) 1 2 b (t t ) I a (t t ) nput (t) = + +- - 2 1 bh(t t ) Output h(t ah(t ) t ) = + +-- - = ) t t ( ) t ( f Input j j - = ) t t ( h ) t ( f Output j j 3 Flip, shift, multiply and integrate Flip and shift one of the two functions. Which one to flip and shift? Either one will do. In the flipped and shifted function, replace by t- Multiplication Integrate from - to + . h(t) f(t) y(t) = ? f(t): Input signal h(t): Impulse response y(t): Output signal y(t) f (t )h( )d f ( )h(t )d f (t) h(t) h(t)*f (t) -- - = - = = 4 h(- ) h( ) h(t-...
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This document was uploaded on 01/13/2012.
- Spring '06