Question

Consider a message signal m(t) with the spectrum shown in the following Figure. The message signal bandwidth W=1KHz, This signal is applied to a product modulator, together with a carrier Accos(2πfc t)wave producing the DSB-SC modulated wave S(t). This modulated wave is next applied to a coherent detector. Assuming perfect synchronism between the carrier waves in the modulator and detector, determine the spectrum of the detector output when: (a) The carrier frequency fc=1.25 KHz. And (b) The carrier frequency fc=0.75 KHz. What is the lowest carrier frequency for which each component of the modulated wave S(t) is uniquely determined by m(t)?

Answer 1

The lowest carrier frequency at which each modulated wave S(t) component may be uniquely defined by m(t) is

Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz

-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz

"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.

Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz

-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz

This is further explained below.

What is the lowest carrier frequency for which each component of the modulated wave S(t) is uniquely determined by m(t)?

For a modulated wave with frequency components, the equation looks like this:

Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz

-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz

"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.

b)

In conclusion, we may state that the modulated wave has frequency components as well.

Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz

-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz

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