You are asked to design a DSB-SC modulator to generate a modulated signal km(t)

Question

You are asked to design a DSB-SC modulator to generate a modulated signal km(t) cos (omega, t), where m(t) is a signal band-limited to B Hz. The figure below shows a DSB-SC modulator available in the stock room. The carrier generator available generates not cos(omega, t) but cos^3 (omega, t). Explain whether you would be able to generate the desired signal using only this equipment. You may Use any kind of filter you like. What kind of filter is required in the figure below? Determine the signal spectra at points b and c. and indicate the frequency bands occupied by these spectra. What is the minimum usable value of omega_c? Would this scheme work if the carrier generator output were cos^2 (omega_c t)? Explain. Would this scheme work if the carrier generator output were cos^x (omega_c t) for any integer n > 2?

Explanation / Answer

a) At filter input you will get m(t)cos3 wct

as cos3 wct=(cos3wct +3 coswct)/4

Thus to extract Cos wct component Low pass filter(LPF) is required.

b) Draw fourier transform of cos3 wct and multiply it with the message spectrum.

c) Minimum usable value of wc =2B as per Nyquist rule

d) This will also work for cos2 wct

As cos2 wct=(1+2cos 2wct )/2

e) It will work for cosn wct with the similar above explaination.

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