Optimal filter design for active noise canceling systems using linear programming in the cepstral domain

A class of simple active noise-canceling algorithms rely on negative feedback techniques [S.J. Elliott et al, 1993 and S.M. Kuo et al, 1999]. In such systems, a microphone captures the combination of the incoming noise and the "anti-noise" emitted by a loudspeaker, and that signal is filtered, amplified, and phase-inverted, then sent back to the loudspeaker. Most commercially available active noise-reduction headphones use negative feedback systems, because they can easily be implemented using analog components, are relatively simple, and can achieve fairly good performance. The problem of designing the filter to be used in the feedback loop isn't simple though: the filter must have a high gain in the frequency region where significant noise attenuation is desirable, but must guarantee that the closed-loop system remains stable. These two constraints run against one another, and to this author's knowledge, no optimal design procedure has yet been proposed to design such filters. This paper presents an algorithm for designing optimal FIR filters (and near optimal IIR filters) to be used in negative-feedback active noise-canceling systems. The algorithm uses the cepstral domain to constrain the filter in both magnitude and phase, and a linear-programming optimization technique to achieve the maximum noise attenuation while maintaining stability