hw1 - Homework 1 ECE 220 Due February 3 2005 With some of...

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Homework 1 ECE 220 Due February 3, 2005 With some of the problems, we reference a relevant worked problem on the CD that comes with your textbook. The worked problems on the CD are just a reference point in the case that you are unsure how to do a problem. These worked problems are indicated by the letters CD followed by the name of the problem. Please do not submit answers for the CD problems. 1. Find the frequency, radian frequency, phase shift, and amplitude of the following three signals: (a) x ( t ) = 5 cos(2 π 500 t + π 2 ) (b) y ( t ) = 10 cos( π 3 ) cos(314( t + 1 100 )), use π = 3 . 14. (c) z ( t ) = (2 + j )(2 - j ) cos( π 250 t + π 3 ) CD: Chapter 2 homework - Determine sinusoidal parameters from a plot. 2. Use the MacLaurin series expansion for e x , cos( θ ) and sin( θ ) to verify Euler’s formula. CD: Chapter 2 Exercise 2.1 3. Use Euler’s formula to prove DeMoivre’s formula. (cos( θ ) + j sin( θ )) n = cos( ) + j sin( ) 4. Simplify the following expressions by putting them in the form Ae .
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