Hw1_sol - 1 ECE 220 Spring07 Signals and Information By...

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Unformatted text preview: 1 ECE 220 Spring07 Signals and Information By Prof. Rick Johnson, Prof. Adam Bojanczyk Solution of Homework # 1 This solution was written by Tae Eung Sung Problem 1 The general representation for a cosine function is as follows: ) 2 cos( ) ( + = t f A t x where A , f , and are the amplitude, (cyclic) frequency, phase shift and radian frequency, respectively. 1) 8 . 2 = A , 8765 = f , 256 = , 17530 = 2) Since cos ) 2 sin( = + , then ) 30 2 cos( 25 . 5 ) ( t t x = . Hence, 25 . 5 = A , 30 = f , 60 = , = . 3) Since 2 ) 1 )( 1 ( = + j j and 2 cos 1 cos 2 2 + = , then ) 16384 2 cos( 2 ) 16384 2 cos( 2 ))) 8192 2 2 cos( 1 ( 1 ( 2 ) ( + = = + = t t t t x . Hence, 2 = A , 16384 = f , 32768 = , = . Problem 2-1-0.8-0.6-0.4-0.2 0.2 0.4 0.6 0.8 1-1-0.5 0.5 1 1.5 2 time t x(t),y(t),z(t) Plots for Problem 2 x(t) y(t) z(t) 2 Problem 3 By Eulers formula sin cos j e j + = , 1) 2 2 2 ) ( ) 2 sin 2 (cos...
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This note was uploaded on 04/17/2008 for the course ECE 2200 taught by Professor Johnson during the Spring '05 term at Cornell University (Engineering School).

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Hw1_sol - 1 ECE 220 Spring07 Signals and Information By...

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