The input x(t) and the output y (t) of a certain communication channel are relat

Question

The input x(t) and the output y (t) of a certain communication channel are related as y(t) = x(t)+ 0.000158x2 Determine whether this channel introduces any distortion over the signal at its output? If no, why? If yes, why and what type of distortion? Assuming that the input signal is x(t) - 2000 sin c(2000 pit), find out the output signal y(t) and its spectrum Y(f). Plot the spectra of the input signal X(f) and the output signal Y(f) assuming the input signal in part (b). What are the bandwidths of the input signal and the output signal?

Explanation / Answer

a) in above question,

relation are non linear, so it gives non linear distortion due to non linear relation.

b)y(t)=x(t)+.000158*x(t)^2

=2000*sinc(2000*pi*t)+.000158*2000^2*((1-cosc(4000*pi*t)/2)

=2000*sinc(2000*pi*t)+632*((1-cosc(4000*pi*t)/2)

its spectrum i can't draw due to lack of camera.....but i can give ans one component will be at o frequecy and first part will have 1khz spectrum left side and right side of origin starting from 0 frequecy.......and second part will have 2khz frequency both side of origin staring from o frequency.

c)x(f) having spectrum both side of origin starting from o frequuency upto 1 khz and Y(f) having same as above said.

bandwith of X(f) is 1khz and bandwith of Y(f) is 2khz.

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