April 2008
Intermediate
832 pages
26h 2m
English
Content preview from Adaptive Filters
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CHAPTER 42 Error-Feedback Lattice Filters
Although the a posteriori- and a priori-based lattice filters of the previous chapter are common lattice forms, several other equivalent implementations exist such as error-feedback forms, array-based forms, and normalized forms. All these variants are, of course, theoretically equivalent. However, they can differ in performance under different operating conditions that arise, for example, in finite-precision implementations or as a result of noise and regularization.
42.1 A PRIORI ERROR-FEEDBACK LATTICE FILTER
In this section we derive the so-called error-feedback form, which tends to exhibit good performance under finite-precision conditions. The algorithm can be motivated as follows. Observe from the a posteriori lattice recursions of Alg. 41.1 that a pivotal role is played by the reflection coefficients 
These coefficients are computed as ratios of certain quantities. For example, 
is computed as the ratio 
, with separate recursions used to evaluate the numerator and denominator quantities. Likewise for .
The error-feedback lattice form ...
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