3. Consider the AM and DSBSC modulated signals given below
V_{AM} = V_c(1 + V_m sin(Δ_m t))sin(Δ_c t)
V_{DSBSC} = V_c V_m sin(Δ_m t) sin(Δ_c t)
a. By expanding the equations for the AM and DSBSC modulated signals, determine the frequency spectrum of the two types of modulation. You may find the following useful:
2 sin(A) sin(B) = cos(A - B) - cos(A + B)
a. What is the bandwidth of the AM modulated signal and what is the purpose of the constant 1? Explain the importance of the knowledge of the AM spectrum for communications engineering.
b. In the Amplitude Modulation (AM), if the carrier is at a frequency of 549 kHz and the modulating signal contains three tones at 1kHz, 2kHz and 3kHz of amplitudes 2.0, 0.5 and 1.0 respectively, sketch the spectrum of AM signal. Is it necessary to transmit both side bands? Explain.