Generate an AR(1) process using the relationship
Xn = 0.9 x Xn-1 + ?n
Where ?n is the output of a Gaussian random number generator (this is option 2 in rangen).
(a) Encode this sequence using a DPCM system with a one-tap predictor with predictor coefficient 0.9 and a three-level Gaussian quantizer. Compute the variance of the prediction error. How does this compare with the variance of the input? How does the variance of the prediction error compare with the variance of the {?n} sequence?
(b) Repeat using predictor coefficient values of 0.5, 0.6, 0.7, 0.8, and 1.0. Comment on the results.