Linear prediction Consider a zero-mean stationary random process x(n) that has the following correlation function: RXn

Linear prediction Consider a zero-mean stationary random process x(n) that has the following correlation function:

RXðnÞ ¼

1 n ¼ 0 0:8 n ¼ 1 0:5 n ¼ 2 0:3 n ¼ 3 0 any other n

:

8>>>>

>>>>:

Linear predictors with two and three delay taps are shown in Figure 7.13.

(a) Determine the coefficients w1 and w2 that minimize the variance of output y(n)

in the predictor given in Figure 7.13(a). What is the variance of output sequence?

(b) Determine the cofficients a1, a2, and a3 that minimize the variance of output y(n) in the predictor given in 7.13(b). Is the variance of output sequence smaller than that in (a)?

Transcribed Image Text:

00 B G F C B A D E G 00 B A G C F D A E EL F D E Figure 7.12 A cellular system with a reuse factor of 7.