Question

(a) A periodic signal x() is represented in Fourier series by the synthesis equation as: x(t)=\sum_{k=-2}^{+2} a_{k} e^{j k \pi r}, \quad \underline{\text { where }}: \quad a_{0}=1 / 2, \quad a_{1}=a_{-1}=2 / 3, \quad a_{2}=a_{-2}=1 / 3 What is the fundamental frequency of x(r)? Express x() in its harmonic complex exponential components. Use Euler's relation to express x() in its harmonic trigonometric (cos, etc.)components. (b) Let the signal x() in part (a), above, be the input to an LTI system with unit impulse response h(t) = e'u(t). Calculate the output response, y(t), making sure you determine the values of its coefficients, bk, corresponding to the given coefficients ak for x(t).

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