Module 6.2: Degradation Estimation

Rewriting (6.2.12), we have

 

 

(6.2.13)

From (6.2.13)

(6.2.14)

and therefore

(6.2.15)

 

The filter in (6.2.15) is called the noncausal Wiener filter. Suppose is uncorrelated with . Then we have

(6.2.16)

From (6.2.16) and noting that are zero-mean processes, we obtain

(6.2.17a)

(6.2.17b)

 

From (6.2.17)

(6.2.18a)
(6.2.18b).