An amplitude-modulated cosine wave is represented by the formula (a) Use phasors to show t...

An amplitude-modulated cosine wave is represented by the formula

(a) Use phasors to show that x(t) can be expressed in the form

 

where ω1 < ω2 < ω3; that is, find values of the parameters A1, A2, A3, φ1, φ2, φ3, ω1, ω2, and ω3.

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(b) Sketch the two-sided spectrum of this signal on a frequency axis. Be sure to label important features of the plot. Label your plot in terms of the numerical values of Ai, φ1, and ω1.