Recent Advances in Digital Filters Based on Allpass Sections

The second order allpass section is the fundamental design unit for filters. In Figures 1 and 2 of [1], it was shown how to realise it with two-port adaptors. Such a realisation, to a certain view, minimises the use of computational resources, having one multiplier per filter order. For VLSI, complexity will in general depend on the number and wordlength of the arithmetic operations involved in the filter. Thus one multiplier per filter order, coupled with the known short coefficient wordlengths possible, promises efficient implementation. Because the sections are recursive the maximum speed (or minimum power through supply voltage scaling [2]) will depend on the critical recursive path. Inspection of the cited figure reveals that this contains two multipliers and six additions. There is an alternative realisation of the second order allpass section, based on 3-port adaptors [3], which has a much shorter critical path. Here this will be reviewed and the pipelining method for the 3-port [4] will be explained in simple stages.