Question

A physical voltage m(t) between a pair of wires modulates a carrier c(t) for transmission as s(t). The system is DSB-PC AM. Part of the message’s spectrum is M(f) = 0.6*exp(j*20)*delta(f-96) + 0.4*exp(j*45)*delta(f-104)+...

But this is not the whole spectrum, for if it were the whole spectrum, then m(t) would be complex, whereas physical voltages cannot be complex

given:

a) Write the whole spectrum M(f). Also, plot |M(f)| and arg M(f).

b) Suppose that the carrier frequency is fc = 800 and that the deviation constant is k = 0.4. Plot |S(f)| and arg S(f). Show your supporting work.

c) your solution included both sidebands of S(f). However, are both sidebands of S(f) really required?

d) why can S(f) omit a sideband even though M(f) cannot? [Hint: like m(t), s(t) too is constrained to be real valued. Explain however why omitting a sideband does not make s(t) complex.]

Answer 1

a) Since is real -

b) Since the system is DSB-PC, the modulated signal is written as -

where is the carrier amplitude.

Hence -

Given . Hence the spectrum can be drawn as -

c) No, both sidebands are not required as both the sidebands carry the same information. Hence removing one of them from the modulated signal causes no problem.

d) It has already been mentioned that is a real signal. Removing any one sideband would lead to a complex signal. Hence we cannot remove a sideband of .

However in the case of , even if we remove one sideband, the other sideband's negative frequency counterpart still remains. Hence the "real" nature of is not changed.