lecture 21

lecture 21 - 1 1 Summary of Lecture #21 10/13/2010...

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Unformatted text preview: 1 1 Summary of Lecture #21 10/13/2010 Convolution integral Flip, shift, multiply and integrate Properties of Delta function, (t), a review Convolution with Delta function Graphical convolution- examples Convolution algebra - - - = - = = d ) t ( h ) ( f d ) ( h ) t ( f ) t ( h ) t ( f ) t ( y 4 t h (1) (t) Ramp, unit step and delta functions 5 h d (t) r(t) tu(t) 1, t u(t) 0, t u(t) u(t) u(t h) dt h lim = = - = = <- Unit step function Ramp function Delta function t t r(t) u( )d tu(t) (12. u(t) ( ) d (12.9 8) ) -- = = = q q dt ) t ( r d ) t ( u = 6 Delta function, (t) A pulse of infinite height, zero width and unit area. Key properties: ) t ( | a | 1 ) at ( ) a T ( f | a | 1 dt ) T at ( ) t ( f ) T ( f dt ) T t ( ) t ( f dt ) T t ( ) t ( f 1 dt ) t ( dt ) t ( T T = =- =- =- = = - - - +- +- 7 Ex. 4. Given f (t) = sin(2 t + ) and h(t) = (t - 5), Find f*h . Ans: y(t) = f(t)*h(t) = sin(2 (t - 5) + ) y(t) f (t) h(t) f (t )h( )d sin(2 ( ) ) ( ) d si t 5 5 n(2 (t ) ) - - - = - = + - = - + 8 Ex. 5. Given f (t) = u(t) + u(t- 1)- 2u(t- 2) and h(t) =- 2 (t- 3), find f*h....
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lecture 21 - 1 1 Summary of Lecture #21 10/13/2010...

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