20072ee132A_1_hwk1_sol

20072ee132A_1_hwk1_sol - EE132A, Spring 2007 Prof. John...

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Unformatted text preview: EE132A, Spring 2007 Prof. John Villasenor Communication Systems TA: Choo Chin (Jeffrey) Tan Handout# 4 Homework 1 Solution Note: Eulers Formula cos sin cos 2 cos sin sin 2 j j j j j j e e e j e e e j j --- + = + =- =- = 1. Evaluate the Fourier transform of the following functions of time: ) ( ) ( ) ( ) 30 2 cos( ) ( ) ( ) ( 3 2 ) ( 1 t u te t s t u t t s t u e t s at b at- +- = + = = r where ) ( t u is the unit step function. (a) Use direct evaluation (a>0) 2 1 1 ( ) 2 ( 2 ) ( 2 ) ( ) ( ) ( ) ( 2 ) 2 j ft at b j ft b a j f t b a j f t b S f s t e dt e u t e dt e e dt e e a j f e a j f -- - +-- -- + -- +- = = = =- + = + You can also use the Fourier Transform table in the text book: { } ( ) 1 1 1 ( ), 2 ( ) ( ) ( ( )) ( ) ( ) 2 at at b b at b b at e u t a a j f s t e u t e e u t e S f e F e u t a j f -- +----- > + = = = = + . (b) Given ( ) 1 t , by using the integration property, 1 1...
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20072ee132A_1_hwk1_sol - EE132A, Spring 2007 Prof. John...

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