The Moog ladder structure is a well known filter used in musical sound synthesizers and in music production. Previously several digital models have attempted to imitate its nonlinear and self-oscillating characteristics. In this paper we derive a novel circuit-based model for the Moog filter and discretize it using the bilinear transform. The proposed nonlinear digital filter compares favorably against Huovilainen's model, which is the best previous white-box model for the Moog filter. The harmonic distortion characteristics of the proposed model match closely with those of a SPICE simulation. Furthermore, the novel model realistically enters the self-oscillation mode and maintains it. The proposed model requires only 12 more basic operations per output sample than Huovilainen's model, but includes the same number of nonlinear functions, which dominate the computational load. The novel nonlinear digital filter is applicable in virtual analog music synthesis and in musical audio effects processing.

Published in the Proceedings of the 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-13), pp. 729-733, May 26-31, 2013, Vancouver, Canada.

• Impulse response from Huovilainen's model (cutoff frequency = 5 kHz, k = 4, input gain = 0.05).
• Impulse response from new model (cutoff frequency = 5 kHz, k = 4, input gain = 0.05).

Unfortunately, there are a few typing mistakes in the equations and figures in this paper. The corrections are available in the following document.

• Errata