Can anyone please help me how to figure out the equation used for \" Gusestimate

Question

Can anyone please help me how to figure out the equation used for " Gusestimate" ? ,and I'm also having a hard time figuring out the sketch, so if possible can you explain the parts of the sketch ? and also what do we consider the area between zero and three on this sketch ?

1. The random binary on-off NRZ signal, x(t), with a value of either 0 or 3 V is shown below. The signal is transmitted in the presence of additive gaussian white noise, n(t) with variance, ?-4, and zero mean. Assume that in x(t), the probability of a 3 is Px(3)0.4 and Px(0)-0.6. Find and sketch the probability density function, pdf, for y(t) x(t) + n(t), and find the signal to noise ratio indB. Note the pdf for n(t) ?s px(n)=ov-e-./ad) and px(x)=k8x) + (1-k)6(x-3) where k is to be determined from the information given for this problem. x(t) n(t) a) Equation for py(y) = anar 16. le e-t-c; b) "Guesstimate" the optimal threshold for detection ? c) SNR (dB)V + Show Work Here +=== Sketch py(y) 4- OS

Explanation / Answer

as stated above that in split phase or manchester coding system "1" is represented by "10" sequence and "0" is represented by "0,-1" sequence for within each clock period. see that DC value here is zero.

in NRZ on the other hand it was "0" or "1" for the entire clock period. we know that clock signal has twice the frequency of that of the NRZ data ad it is "1" for the fiirst T/2 and "0" for the next T/2 time. so if we invert that we will be getting "0" for the first T/2 time and "1" for the next T/2 time.

so, it is very obvious that for the "1" signal if we substract "1" of NRZ data with the inverted clock which has "0" and "1" for T/2 time each we will get back the original clock signal, which will be "1" for the first T/2 and "0" for the next T/2 time.

similarly for the zero it can easily be seen that if we substract from the inverted clock it will be "0" for the first T/2 and "-1" for the next half.

so, combining both together we will get the mancheter coded data which will be "1" for "10 " sequence and "0" for "0-,1" sequence within each clock period.

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