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.

Submitted for publication.

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

[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.