Midterm 3 Solutions

# Furthermore it is gaussian since the samples are from

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Unformatted text preview: samples are from a continuous-time Gaussian process. e) Now we are looking at samples 1=4W seconds apart. The time di erence between any two samples is k=4W where k is an integer. Therefore, RY n] (k) = RY (k=4W ) = N0 W sinc( k ) 2 f) Finding the optimal linear predictor consists of solving the Yule-Walker equations for the set of predictor coe cients fai gjp . Since we are only predicting the current sample from the previous sample, p is 1, which i =1 means that there is only one coe cient a to solve for. aRY n] (1 1) = RY n] (1) R (1) a = RY n] (0) Y n] 0 W sinc (1=2) At rate 2W , a = N0 W 1]] = 0. At rate 4W , a = NN0 W sinc(0) = sinc(1=2) = 2= . It is evident that using N0 W 0 DPCM for the 4W case is more bene cial than using PCM because consecutive samples are correlated. However, using DPCM for the 2W case provides no bene ts because consecutive samples are uncorrelated. In this case, we cannot predict the value of the current sample from the value of the previous sample. Problem 3 a) Here's the picture of fX (x),...
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## This document was uploaded on 01/24/2014.

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