In class we saw an example of 'Beat note'. In this problem we consider a more general case. Let fc > 0, fd > 0 and define a signal x as
x(t) = Acos(2pi(fc - fd)t) + Bcos(2pi(fc + fd)t)
(a) Use phasors to obtain a complex signal z(t) such that x(t) = R(z(t))
(b) By manipulating the expression for z(t) and then taking the real part, show that x(t) can be expressed in the form
x(t) = Ccos(2pi*fd*t)cos(2pi*fc*t) + Dsin(2pi*fd*t)sin(2pi*fc*t) and find expressions for C and D in terms of A and B.
(c) Find values of A and B so that x(t) = 2sin(2pi*fd*t)sin(2pi*fc*t). Plot the spectrum of signal.