Q1. The baseband modulating signal vm (t) is shown in F

Q1.
The baseband modulating signal vm (t) is shown in Figure 1 and it is given by:
vm(t) = 5 cos (2000pt + 20) + 9 cos (6000pt + 600) + 13 cos (10000pt + 1000) + 0.5 cos (14000pt + 1400)
(a) Neatly sketch the magnitude spectrum of vm(t). Clearly label axes and spectral components.
(b) Neatly sketch the phase spectrum of vm(t). Clearly label axes and spectral components.
(c) Standard amplitude modulation is used for transmission using a carrier given by:
vc (t) = 50 cos (50000pt)
What will be the maximum positive value and the minimum positive value of the modulated wave v(t).
Calculate the effective modulation index of v(t).
Sketch the magnitude spectrum of the modulated wave v(t). Indicate on the spectrum the bandwidth of v(t).
Calculate the total power in v(t) if the load resistance is 100 ?.
(d) A baseband modulating signal vm(t) = Vm cos (2pfmt) amplitude modulates a carrier vc(t) = Vc cos (2pfct). Use spectral diagrams and algebraic expressions to compare the 3 methods of amplitude modulation based on the criteria of bandwidth and power usage. On the basis of your explorations indicate which method is most efficient with respect to (i) bandwidth and (ii) power utilization.
Figure 1: Baseband Signal for Question 1
Q2.
Determine the Fourier Transform of the aperiodic message signal shown in Figure 2.
Draw the spectrum of the signal shown in Figure 2.
Include FT in the MATLAB exercise.
Determine the Fourier Series representation of the periodic message signal shown in Figure 3 in both the exponential and trigonometric forms.
(Full marks will be awarded for conversion from one form to another)
Draw the spectrum of the signal shown in Figure 3 up to and including the 5th harmonic.
Figure 2: Message Signal for Q2. (a) and (b)
Figure 3: Message Signal for Q2. (c) and (d)
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