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20115ee102_1_hw4

# 20115ee102_1_hw4 - 1 EE102 Fall Quarter 2011 Systems and...

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1 EE102 Systems and Signals Fall Quarter 2011 Jin Hyung Lee Homework #4 Due: Wednesday, November 2, 2011 at 5 PM. 1. Suppose that f ( t ) is a periodic signal with period T 0 , and that f ( t ) has a Fourier series. If τ is a real number, show that f ( t - τ ) can be expressed as a Fourier series identical to that for f ( t ) except for the multiplication by a complex constant, which you must find. 2. Switching amplifiers are a very efficient way to generate a time-varying output voltage from a fixed supply voltage. They are particularly useful in high-power applications. The basic idea is that an output voltage a is generated by rapidly switching between zero and the supply voltage A . The output is then lowpass filtered to remove the harmonics generated by the switching operation. For our purposes we can consider the lowpass filter as an integrator over many switching cycles, so the output voltage is the average value of the switching waveform.. Varying the switching rate varies the output voltage. In this problem we will only consider the case where the desired output voltage is constant.

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20115ee102_1_hw4 - 1 EE102 Fall Quarter 2011 Systems and...

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