A periodic signal is given by the equation (a) Determine the fundamental frequency ω0, the...

A periodic signal is given by the equation

(a) Determine the fundamental frequency ω0, the fundamental period T0, the number of terms N, and the coefficients ak in the finite Fourier representation (3.37) for the signal x(t) above. It is possible to do this without evaluating any integrals.

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(b) Sketch the spectrum of this signal indicating the complex amplitude of each frequency component. Indicate the complex amplitude values at the appropriate frequencies. There is no need to make separate plots for real/imaginary parts or magnitude/phase.

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(c) Now consider a new signal defined by adding one more sinusoid y(t) = x(t) + 10 cos(50πt − π/6). How is the spectrum changed? Is y(t) still periodic? If so, what is the fundamental period?