Adaptive Filters

CHAPTER 43 Array Lattice Filters

The interpretations we provided for the coefficients in sec 42.1, in terms of solutions to first-order least-squares problems, can be used to motivate yet an other lattice implementation in array form. We discussed array methods and their advan tages in some detail in Chapter 33. We show here that such array methods can also be developed for order-recursive problems.

Thus, recall that in Sec. 42.1 we introduced the angle-normalized estimation errors

and the corresponding angle-normalized error vectors

We then argued that the reflection coefficients can be interpreted as the solutions to three simple (regularized) projection problems, namely

That is, each of these reflection coefficients solves the problem of projecting one angle-normalized error vector onto another. More specifically, they solve the following regular ized least-squares problems:

(43.1)

where

The above interpretations were used in Sec. 42.1 to show that the reflection coefficients ...