In Section 3-2.2, we discussed a simple example of the “beating” of one cosine wave agains...

In Section 3-2.2, we discussed a simple example of the “beating” of one cosine wave against another. In this problem, we consider a more general case. Let

For the case discussed in Section 3-2.2, the amplitudes are equal, A = B = 1.

(a) Use phasors to obtain a complex signal z(t) such that

 

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(b) By manipulating the expression for z(t) and then taking the real part, show that in the more general case above, x(t) can be expressed in the form

 

and find expressions for C and D in terms of A and B. Check your answer by substituting A = B = 1.

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(c) Find values for A and B so that

 

Plot the spectrum of this signal.