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Unformatted text preview: 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 + a 1 x + a 2 x 2 + a 3 x 3 + · · · If we apply an input x ( t ) = cos( ω t ) ideally we would get an output spectrum that looks like ω- ω- 2 ω- 3 ω 3 ω 2 ω 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 t ). Hint: What does the spectra of cos n ( t ) look like for different n ? Don’t integrate! 1 a) Find the output Fourier series spectrum when the amplifier characteristic is y = x + 0 . 1 x 3 ....
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- Spring '08
- Fourier Series, Dirac delta function, series A