Problem 1 (5 Points): Let the following periodic signal x(t) = ?_{k=-?}^{?} [?(t - 3k) + ?(t - 3k - 1) - ?(t - 3k - 2)] be the input to an LTI system with frequency response H(j?) = e^{j?/4} - e^{-j?/4}. Let y(t) be the corresponding output signal. a) (1 Points) Determine the fundamental period of x(t). b) (2 Points) Let ak be the Fourier series coefficients of x(t). Find a closed-form expression for ak. c) (2 Points) Let bk be the Fourier series coefficients of y(t). Determine the numerical value of b3.
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