Electrical Engineering 20N - Fall 2001 - Lee - Midterm 2

# Electrical Engineering 20N - Fall 2001 - Lee - Midterm 2 -...

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EE 20N, Midterm #2, Fall 2001 EE 20N Fall 2001 Midterm #2 Professor Edward Lee Problem #1 20 points. Consider a continuous-time signal x : Reals -> Reals defined by For all t in Reals , x ( t ) = cos( omega 1 t ) + cos( omega 2 t ), where omega 1 = 2*pi and omega 2 = 3*pi radians/second. (a) Find the smallest period p in Reals + , where p > 0. (b) Give the fundamental frequency corresponding to the period in (a). Give the units. (c) Give the coefficients A 0 , A 1 , A 2 , . .. and phi 1 , phi 2 , . .. of the Fourier series expansion for x . Problem #2 30 points. Suppose that the continuous-time signal x : Reals -> Reals is periodic with period p . Let the fundamental frequency be omega 0 = 2*pi / p . Suppose that the Fourier series coefficients for this signal are known constants A 0 , A 1 , A 2 , . .. and phi 1 , phi 2 , . .. . Give the Fourier series coefficients A ' 0 , A ' 1 , A ' 2 , . .. and phi ' 1 , phi ' 2 , . .. for each of the following signals: (a) ax , where a in Reals is a constant (b) D

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Electrical Engineering 20N - Fall 2001 - Lee - Midterm 2 -...

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