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). |
|