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

An amplitude-modulated (AM) 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. In addition, find values for the parameters A1, A2, A3, φ1, φ2, φ3, ω1, ω2, ω3.

---

(b) Sketch the two-sided spectrum of this signal on a frequency axis. Be sure to label important features of the plot, and include the numerical values of the parameters Ai, φi, and ωi for i = 1, 2, 3.

---

(c) Determine the minimum sampling rate that can be used to sample x(t) without aliasing of any of the components.