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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)?

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okpalawalter8

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

  • [tex]-Fc,-Fc+W,-Fc-wW = > -1.5k,-0.5k,-2.5kHz[/tex]

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

  • [tex]-Fc,-Fc+w,-Fc-W = > -0.75k,0.25k,-1.75kHz[/tex]

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)?

Generally, the equation for the modulated wave containing frequency components  is  mathematically given as

[tex]Fc,Fc+w,Fc-W = > 1.5k,2.5k,0.5kHz[/tex]

[tex]-Fc,-Fc+W,-Fc-wW = > -1.5k,-0.5k,-2.5kHz[/tex]

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

b)

In conclusion,, then the modulated wave contains frequency components as

[tex]Fc,Fc+W,Fc-W = > 0.75k,1.75k,-0.25kHz[/tex]

[tex]-Fc,-Fc+w,-Fc-W = > -0.75k,0.25k,-1.75kHz[/tex]

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