hw7 - Assignment#7 ECSE-2410 Signals Systems Fall 2005 Due...

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Assignment #7 ECSE-2410 Signals & Systems - Fall 2005 Due Fri 09/30/05 1. (30) Using only properties of Fourier series, compute the exponential Fourier series coefficients b k for the triangular function y(t) of period 3 pictured below. That is, write y(t) in the form -∞ = ϖ = k t jk k e b t y 0 ) ( . Hint: what is the derivative of y(t) ? 2. (30) In Matlab, plot the signal y(t) from #1 vs. t for t = [-2,3]. Then on the same graph, plot the approximation - = ϖ = N N k t jk k N e b t y 0 ) ( for N =1, N =3, N =5, and N =15. Plot the N =15 curve in red so you can see how good the approximation is. Attach the plot to your homework and describe what you see. (You should only hand in one plot for this question, with the five functions on the same graph.) Make sure your name is in the title of your plot. (see reverse for a few Matlab commands) 3. (40) Find the Fourier transform for each the signals below, directly using the definition of the Fourier transform [Equation (4.9) in O&W].
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