HW2 - ( w jw w H + = Problem 5 : Assume the input signal is...

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ECE 45 Fall 2007 Homework #2 Due Tuesday, Oct. 23, 2007 Note : You should solve each of these problems without a calculator. For phase shift calculations, you may leave your answer in terms of tan -1 (x). As an example, your output function can be written as such: f(t) = 2cos(5t + 10° - tan -1 (5/2)). Problem 1 : Kudeki 5.2 Problem 2 : Kudeki 5.11. Change f(t) to f(t) = 4 + cos(t). Problem 3 : Kudeki 5.9. Change f(t) in part (c) to f(t) = cos(t-10°) + 2sin(3t). Problem 4 : Sketch the Bode plots (both magnitude and phase) for each frequency response expression below. Use the Bode plot paper from the website for your final plots. (a) ) 10 1 )( 10 1 )( 10 1 ( 10 ) ( 5 2 4 jw jw jw jw w H + + + = (b) 2 2 11 10 10 )
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Unformatted text preview: ( w jw w H + = Problem 5 : Assume the input signal is given by 2 2 ( ) 4 3cos( ) 7sin( ) 2 2 j t j t x t t t je je = + + + (a) What is the fundamental frequency, w o , of x(t)? (b) Write the Fourier series representation of x(t). (c) What are the Fourier coefficients X n of x(t)? (d) Using (a) and (b), find the output response y(t) given that the frequency response is = , , 5 . ) ( w H otherwise w 1 | | Problem 6 : What is the fundamental period T o and fundamental frequency w o of the signal f(t) below? Calculate the Fourier coefficients F n . . . . . . . f(t) t 1 1 2 -1 -1 H(w) x(t) y(t)...
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