Extended properties of the Levinson recursion and lattice filters

The direct parallels between the z-transform and the Levinson recursion, such as complex conjugation, sequence reversal, upsampling, and modulation by a complex exponential of unity magnitude, are explored, and the effects on the associated lattice filter structures are investigated. The modulation property of a general complex exponential for the z-transform is extended to the lattice filter with a systematic modification of the reflection coefficients of the filter. A reciprocal-based lattice filter is derived. It has the structure of a standard lattice filter yet the zeros of the system function depend explicitly on the weighting functions of the filter. This filter has the property that the system function roots remain fixed as additional sections are added to the filter.<>