A band limited randomsignal of band width 10kHz is uniformly distributed over the range(-1,+1) VOLT, it is sampled at twice Nyquist rate and quantizedinto Q levels. The samples are binary PCM encoded into n bits whichare transmitted using two waveforms S1 (t)=1.414 sin(w1t) and S2(t)=1.414 sin(w1t) + 1.414 cos(w1t) where t is between 0 and Tb,and the a priory probability of S1 is p(s1) = 0.4. Abinary matchedfilter receiver is used and a WGN is added with No=E(-7)w/Hz.
a) Find the number of binary digits n required to have BER=E(-4)
b) find the ratio of message signal power of m(t)to the noise output due to channel error and quantization error indB.
c) Find the signal to qunatization error ratio, and signal to channelerror ratio and comment.
d) Suggest a minimum modification for the waveforms to gain some advantages for the same error probability, and specify thisadvantages. Find also the effect of this modification on the resultobtained in (b) above.