EN.580.223 Final: Final Solutions Fall 2011
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A periodic signal x t (saw-tooth wave) with fundamental period t = 4 is defined over one period as: x t t. The fourier series coefficients of are represented by kx : (5 points) determine the value of. Since the signal is odd and there is no direct component, a. 0: (5 points) determine the value of. Show your work. (hint: start with the k k. Fourier series representation of and remove the exponential term by evaluation at a particular value of . ) To get a , we set k i. The input-output relationship of an lti system is described by the following differential equation at rest: , if the input x t sin 2 t ? (hint: find a representation for or first. ) The fundamental frequency is 0 1 f x t has two exponential components with k. The following is an lti system with impulse response h t cos 2 t . x(t)
