Generalized Moog Ladder Filter: Part II - Explicit Nonlinear Model through a Novel Delay-Free Loop Implementation Method

Title
Generalized Moog Ladder Filter: Part II - Explicit Nonlinear Model through a Novel Delay-Free Loop Implementation Method
Authors
Stefano D'Angelo and Vesa Välimäki
Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering Espoo, Finland
Abstract
One of the most critical aspects of virtual analog simulation of circuits for music production consists in accurate reproduction of their nonlinear behavior, yet this goal is in many cases difficult to achieve due to the presence of implicit differential equations in circuit models, since they naturally map to delay-free loops in the digital domain. This paper presents a novel and general method for non-iteratively implementing these loops in such a way that the linear response around a chosen operating point is preserved, the topology is minimally affected, and without requiring transformation of nonlinearities. Such technique is then applied to a generalized version of the Moog ladder filter, resulting in an implementation that clearly outperforms its predecessors with only a modest computational load penalty. This digital version of the filter also allows the extraction of different frequency response modes by simple mixing of its outputs and is suitable for real-time sound synthesis and audio effects processing.
Status
Submitted for publication.
Sound samples
Description Input Huovilainen [1] Previous [2] Proposed SPICE
Audio-rate natural cutoff parameter variation test #1, with 440 Hz sinusoidal input signal of amplitude 1, fs=96 kHz, k=4, sinusoidal natural fc signal from 20 Hz to 10 kHz with modulation frequency 146.66... Hz fmin.wav fm1h.wav fm1p.wav fm1m.wav fm1s.wav
Audio-rate natural cutoff parameter variation test #2, with 440 Hz sinusoidal input signal of amplitude 1, fs=96 kHz, k=4, sinusoidal natural fc signal from 20 Hz to 10 kHz with modulation frequency 1320 Hz fm2h.wav fm2p.wav fm2m.wav fm2s.wav
Input amplitude variation test, with 10-s long 440 Hz sinusoidal input signal of amplitude 0 to 1, fs=96 kHz, k=4, natural fc=12 kHz ain.wav ah.wav ap.wav am.wav as.wav
Music input signal test #1, input signal scaled to range -0.1 to 0.1, fs=48 kHz, k=0, natural fc from 20 Hz to 6 kHz, normalized output level sample.wav h0.wav p0.wav m0.wav s0.wav
Music input signal test #2, input signal scaled to range -0.1 to 0.1, fs=48 kHz, k=2, natural fc from 20 Hz to 6 kHz, normalized output level h2.wav p2.wav m2.wav s2.wav
Music input signal test #3, input signal scaled to range -0.1 to 0.1, fs=48 kHz, k=4, natural fc from 20 Hz to 6 kHz, normalized output level h4.wav p4.wav m4.wav s4.wav
References
[1] A. Huovilainen, "Non-linear digital implementation of the Moog ladder filter," in Proc. 7 th Intl. Conf. Digital Audio Effects (DAFx-04), Naples, Italy, October 2004, pp. 61-64.
[2] S. D'Angelo and V. Välimäki, "An improved virtual analog model of the Moog ladder filter," in Proc. Intl. Conf. on Acoustics, Speech, and Signal Process. (ICASSP 2013), Vancouver, Canada, May 2013, pp. 729-733.

 

http://www.acoustics.hut.fi/publications/papers/ieee-taslp-2014-moog/
Author: Stefano D'Angelo
Modified: 5.5.2014, Stefano D'Angelo

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