Using the same assumptions on X(jω)and ωc as in Prob. P-12.8, consider the case when the m...

Using the same assumptions on X(jω)and ωc as in Prob. P-12.8, consider the case when the modulator and demodulator are in phase (ϕ = 0) bot the demodolator carrier frequency is mismatched by a small amount ∆ ⟪ ωc as depicted in the block diagram in Fig. P-1.

Figure P-1

(a) Make a plot of W(jω)for the bandlimited X(jω)given in Prob. P-12.8.

(b) Use this plot to help you determine an equation for υ(t)in term s of x(t)and ∆. In this case , you will need to assume that the cutoff frequency of the ideal lowpass filter satisfies (ωb + ∆)<ωco<(2ωc + ∆ – ωb).