# HW13

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Signals and Systems 14 November 2012 Fall 2012 Quiz: Wednesday 21 November 2012 Homework Assignment #13 1. Compute the coefficients of the exponential Fourier series expansion for the functions given on the interval [0, T ]. For each case, sketch the amplitude spectrum | α n | and sketch the function represented by the Fourier series for T t 2 T. (a) Ω Ψ Χ = T t T T t A T t At t x 2 / ), ( 2 2 / 0 , 2 ) ( (Triangular wave) (b) Ω Ψ Χ = T t T T t T t A t x 2 / , 0 2 / 0 ), / 2 sin( ) ( π (Half-wave rectified sinusoid) 2. Let x ( t ) be a square wave. Use a digital computer to plot an approximation to x ( t ) consisting of the first 5, 10, and 15 terms of the Fourier series for a square wave, as given in Table 3.1. 3. Repeat problem 2 if x ( t ) is a triangular wave. For which wave (square or triangular) do
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