## 12.3 DIGITAL BASIC LATTICE FILTERS

Digital lattice filters are composed of regular modules. If the order of a filter is *N,* then *N* modules are needed. The lattice filter that realizes any transfer function can be viewed as a filter with the property that if the denominator polynomial is fed into the filter, the numerator polynomial is obtained at the output node. The essence of this synthesis procedure is based on the *polynomial degree reduction,* which means that the degree of these polynomials will be reduced by one after passing through each module. After *N* modules, the polynomials have degree zero and are just constants. By matching these constants, we can simply interconnect them by appropriate multipliers.

In this section, 2 slightly different basic lattice filter structures are derived. The 1st one is derived using the Schur polynomials and the 2nd one is derived using the reverse Schur polynomials.

### 12.3.1 Derivation of Basic Lattice Filters

The Schur polynomials are obtained by using the degree reduction procedure

where *s*_{i} is any nonzero scaling factor and

If we choose

then the Schur polynomials {**Φ**_{N}(*z*), **Φ**_{N−1}(*z*), · · ·, Φ_{0}(*z*)} are orthonormal to each other and can be used ...