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102_1_final_practice

# 102_1_final_practice - Systems and Signals EE102 Lee Spring...

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Systems and Signals Lee, Spring 2009-10 EE102 Final Practice Problem 1. Fourier Series A linear amplifier has an output y that is proportional to the input x , y = a 1 x where a 1 is a constant. In practice an amplifier will have a more complex characteristic y = a 0 + a 1 x + a 2 x 2 + a 3 x 3 + · · · If we apply an input x ( t ) = cos( ω 0 t ) ideally we would get an output spectrum that looks like ω 0 - ω 0 - 2 ω 0 - 3 ω 0 3 ω 0 2 ω 0 0 ω 1 2 where we’ve assumed a 1 = 1 for simplicity. In practice we get something different, and this tells us something about the amplifier char- acteristic. For each of the following amplifier characteristics, determine what the output Fourier series spectrum looks like when the inputs is x ( t ) = cos( ω 0 t ). Hint: What does the spectra of cos n ( t ) look like for different n ? Don’t integrate! 1

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a) Find the output Fourier series spectrum when the amplifier characteristic is y = x + 0 . 1 x 3 . ω 0 - ω 0 - 2 ω 0 - 3 ω 0 3 ω 0 2 ω 0 0 ω 1 2 2
b) Find the output Fourier series spectrum when the amplifier characteristic is y = - 0 . 1 + x + 0 . 2 x 2 ω 0 - ω 0 - 2 ω 0 - 3 ω 0 3 ω 0 2 ω 0 0 ω 1 2 3

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Problem 2. Sampling Timing Errors
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102_1_final_practice - Systems and Signals EE102 Lee Spring...

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