Consider a discrete-time, analog sourcewith memory,i.e.,U1, U2, . . .are dependent rv's.
Assume that each Uk is uniformly distributed between 0 and 1 but that U2n=U2n-1for
each n=1. Assume that{U2n}8are independent. n=1
(a) Find the one-bit (M= 2) scalar quantizer that minimizes the mean-squared error.
(b) Find the mean-squared error for the quantizer that you have found in (a).
(c) Find the one-bit-per-symbol (M= 4) two-dimensional vector quantizer that minimizes the MSE.
(d) Plot the two-dimensional regions and representation points for both your scalar quantizer in part (a) and your vector quantizer in part (c).