Fixed-point implementation of Lattice Wave Digital Filter: Comparison and error analysis

A consistent analysis of the filter design along with its further implementation in fixed-point arithmetic requires a large amount of work, and this process differs from one filter representation to another. For the unifying purposes of such flow, a Specialized Implicit Form (SIF) had been proposed in [1]. Various sensitivity and stability measures have been adapted to it along with an a priori error analysis (quantization of the coefficients and output error). In this paper a conversion algorithm for the widely used Lattice Wave Digital Filters (LWDF) to the SIF is presented, along with a finite precision error analysis. It allows to compare fairly LWDF to other structures, like direct forms and state-space. This is illustrated with a numerical example.