Question

of the LSB spectrum plucedure to also find PuSB ). A modulating signal m(t) įs given by: (a) m(1)=cos 100π 1+2cos 300 (b) m()= sin 10Ort sin 500ml In each case: (i) Sketch the spectrum of m(t). (ii) Find and sketch the spectrum of the DSB-SC signal 2m(r) cos 1000 4.4.3 . ppress the LSB spectrum to obtain the USB spectrum. (iv) Knowing the USB spectrum in part (i), write the expression pusa(0) for the USB signal (v) Repeat parts (lii) and (iv) to obtain the LSB signal prSB() in both time and frequency domains.

Answer 1

Given that (a) m(t) = cos 100 pi t + 2 cos 300 pi t (i) Spectrum of m(t): - Fourier transform of m(t) m(f) = 1/2 [S(f - 50) + S(f + 50)] + 2 times 1/2 [S(f - 50) + S(f + 50)] F.T. [cos 2 pi f_0 t] = 1/2 [S(f - f_0) + S(f + f_0)] M(f) = 1/2 [S(f - 50) + S(f + 50)] + S(f - 50) + S(f + 50) (ii) DSB - SC Signal 2m(t) cos 1000 pi t = S(t) S(t) = 2 [cos 100 pi t + 2 cos 300 pi t] cos 1000 pi (t) S(t) = 2 cos 1000 pi t + cos 100 pi t + 4 cos 1000 pi t + cos 300 pi t Therefore 2 cos A cos B = cos(A + B) + cos(A - B) \r\n DSB-SC signal S(t) = cos 1100 pi t + cos 900 pi t