Reference no: EM132165900

Question 1: A DSB-SC modulation generates a signal φ(t) = A_cm(t)cos(ω_ct + θ).
(a) Sketch the amplitude and phase spectra of v(t) for φ(t) = Δ(200t).
(b) Sketch the amplitude and phase spectra of f ,o(t) for φ(t) = Δ(100t -50).

Question 2: Consider the following baseband message signals (i) m₁(t) = sin 150Πt; (ii) m₂(t) = 2exp(-2t)u(t); (iii) cos200Πt + rect(100t); (iv) m(t) = 50exp(-100|t|) . sgn(t); and (v) m(t). 500exp(-100|t| - 0.5). For each of the five message signals,
(a) sketch the spectrum of m(t);
(b) sketch the spectrum of the DSB-SC signal 2m(t)cos 200Πt;
(c) identify the USB and the LSB spectra.

Question 3: Amplitude modulators and demodulators can also be built without using multipliers. In Fig. P4.2-8, the input #(0 = m(t), and the amplitude A >>10(01. The two diodes are identical with a resistance r ohms in the conducting mode and infinite resistance in the cutoff mode.

Define the switching signal w(t) as in Fig. 4.4b with period 2Π/ω_c seconds.

(a) Show that the voltages on the two resistors are approximately equal to

[Φ(t) + A cosω_ct].w(t).R/(R + r)

[Φ(t) + A cosω_ct].w(t)R/(R + r)

Hence, e_o(t) is given by

e_o(t) = 2R/(R + r). w(t)Φ(t)

(b) Moreover show that this circuit can be used as a DSB-SC modulator.

(c) Explain how to use this circuit as a synchronous demodulator for DSB-SC signals.

Question 4: Sketch the AM signal [B +m(t)] cosω_ct for the random binary signal m(t) shown in Fig. P4.3-1 corresponding to the modulation index by selecting a corresponding B: (a) μ = 0.5; (b) μ = 1; (c) μ = 2: (d) μ = ∞. Is there any pure carrier component for the case μ = ∞?

Figure