A periodic signal is given by the equation x (t) = 2 + 4 cos (40 ? t - ?/5) + 3

Question

A periodic signal is given by the equation x (t) = 2 + 4 cos (40 ? t - ?/5) + 3 sin (60 ? t) + 4 cos (120 ? t - ?/3)

A. Determine the fundamental frequency w0, the period t0, and the coefficients in the representation X(t) = x0 + Re{?k=1N Xkejkwot} for the above input. Remember, you can do this problem without evaluating any integrals.

B. Sketch the spectrum of this signal indicating the complex size of each frequency component. You do not have to make separate plots for real/imaginary parts or magnitude/phase. Just indicate the complex phasor value at the appropriate frequency.

C. Now consider a new signal y(t) = x(t) + 10 cos (50 ? t - ?/6). How is the spectrum changed? Is y(t) periodic? If so, what is the period?

Explanation / Answer

A. fundamental frequency fo = 120/2pi wo =120 to= 2pi/120 B. put sine and cos separated sin component will be imaginary and cos will be real . C. spectrum frequency will be changed . yes it is all periodic with period= 2pi / 600

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