A signal composed of sinusoids is given by the equation (a) Sketch the spectrum of this si...

A signal composed of sinusoids is given by the equation

(a) Sketch the spectrum of this signal, indicating the complex amplitude of each frequency component. Make separate plots for real/imaginary or magnitude/phase of the complex amplitudes at each frequency.

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(b) Is x(t) periodic? If so, what is the period?

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(c) Now consider a new signal defined as y(t) = x(t) + 5 cos(1000πt + n/2). How is the spectrum changed? Is y(t) periodic? If so, what is the period?