A First Experimental Study of Fixed-Point Approximate Arithmetic in Recursive Lattice Filters

In some situations, the numerical properties of Direct Form I (DF-I) and Direct Form II (DF-II) Infinite Impulse Response (IIR) filter structures may degrade, e.g., when the filter approaches its stability limit. Other filter structures may be numerically more robust under such conditions. For example, an Nth order Lattice filter composed of N structurally identical cascaded feed-forward sections can be extended and made recursive, i.e., Lattice IIR filter, thereby implementing zeros as well as poles. Such filters, however, have a significantly higher computational complexity compared to their DF-I and DF-II counterparts, increasing the execution time and the energy consumed per sample period. Approximate Computing (AxC) applied in Lattice IIR filters has not been researched in the scientific literature to date, and therefore we suggest substituting the exact fixed-point multiplications and additions with AxC arithmetic building blocks to potentially reduce the resource overhead. In this first study, we analyze the numerical consequences of using such arithmetic units in the 2nd order recursive Lattice structure and compare its performance against the ordinary DF-II structure. Our findings clearly indicate that under certain conditions AxC arithmetic is a useful approach in recursive Lattice filters.