Improving the Chamberlin Digital State Variable Filter

TL;DR

This paper analyzes and improves the digital Chamberlin state variable filter, enhancing its spectral shaping capabilities through new transfer functions and comparing different implementation approaches.

Contribution

It derives new transfer functions for the Chamberlin filter and proposes an improved design to better shape the filter spectrum.

Findings

Enhanced spectral response of the filter

New transfer functions derived and validated

Comparable performance with alternative implementation methods

Abstract

The state variable filter configuration is a classic analogue design which has been employed in many electronic music applications. A digital implementation of this filter was put forward by Chamberlin, which has been deployed in both software and hardware forms. While this has proven to be a straightforward and successful digital filter design, it suffers from some issues, which have already been identified in the literature. From a modified Chamberlin block diagram, we derive the transfer functions describing its three basic responses, highpass, bandpass, and lowpass. An analysis of these leads to the development of an improvement, which attempts to better shape the filter spectrum. From these new transfer functions, a set of filter equations is developed. Finally, the approach is compared to an alternative time-domain based re-organisation of update equations, which is shown to deliver a similar result.