The "ARMAdillo" Coefficient Encoding Scheme for Digital Audio Filters

Abstract

In the &sign of VLSI circuits to implement digital filters for electronic music purposes, we have found it useful to encode the filter coefficients. Such encoding offers three advantages. First, the encoding can be made to correspond more properly to the "natural" perceptual units of audio. While these are most accurately the "bark" for frequency and the "sone" for loudness, a good working approximation is decibels and musical octaves respectively. Secondly, our encoding scheme allows for partial decoupling of the pole radius and angle, providing superior interpolation characteristics when the coefficients are dynamically swept. Thirdly, and perhaps most importantly, appropriate encoding of the coefficients can save substantial amounts of on-chip memory. While audio filter coefficients typically require twenty or more bits, we have found adequate coverage at as few as eight bits, allowing for a much more cost effective custom hardware implementation when many coefficients are required. We have named the resulting patented encoding scheme "ARh4Adillo." Our implementation of digital audio filters is based on the canonical second order section whose transfer function should be familiar to all: 1*-1*-2 H(Z) = +blz-1+b,z-2 [I1 While dealing with poles and feedback (bn) coefficients, the comments herein apply as well to zeroes and feedforward coefficients (an/@) when the gain (a@ is separated as shown above. Noting that the height of a resonant peak in the magnitude response produced by a pole is approximately inversely proportional to the distance from the pole to the unit circle, we can relate the height p of this resonant peak in dB to the pole radius R: 1 1-R