VLSI Digital Signal Processing Systems: Design and Implementation

12.1    INTRODUCTION

This chapter addresses the design of lattice digital filters. Four types of lattice digital filters are presented: basic, 1-multiplier, normalized and scaled-normalized. Although the major emphasis of this chapter is on design of IIR lattice filters, the techniques can also be used to design FIR lattice filters. Design of FIR lattice filters is illustrated only in the context of basic lattice digital filters.

The simplest form of the IIR digital filter structures is the direct-form structure, where the numerator and the denominator coefficients are directly used as multiplier coefficients in the implementation. However, this structure has very high sensitivity, because the roots of a polynomial are very sensitive to the coefficients, so the poles and zeros of the given transfer function are very sensitive to the quantized multiplier coefficients [1]. With standard filters such as low-pass, high-pass, and band-pass, the poles are generally crowded at angles close to the band edge. Sensitivity of the structure becomes worse as the number of crowded poles increases. This sensitivity problem can be avoided by implementing the transfer function as a sum or product of 1st and 2nd-order sections, i.e., parallel or cascade form structures. However, for complex conjugate poles with small angles (e.g., narrow-band sharp-transition filters), we still have high sensitivity problems even with 2nd-order sections.

However, the lattice digital filters have good numerical properties ...