Paschou, Esqueda, Välimäki & Mourjopoulos — Modeling and Measuring a Moog Voltage-Controlled Filter (APSIPA ASC 2017)
Effrosyni Paschou (Aalto University Acoustics Lab / University of Patras), Fabián Esqueda and Vesa
Välimäki (Aalto), John Mourjopoulos (Patras). Proc. 9th APSIPA Annual Summit and Conference, pp.
1641–1647, IEEE 2017, DOI 10.1109/APSIPA.2017.8282295. Read in full from the Aalto repository
post-print with pypdf after the publisher PDF would not extract in-browser.
This is the bench comparison the spoke's edge asked for, and the thing moog-ladder-nonlinear-digital explicitly was not: a digital ladder-filter model put next to a real Moog and measured against it.
What was measured, on what
The analog side is a Moog Mother-32, a synthesizer sold today with the ladder circuit in it — not a vintage unit and not a SPICE netlist. Everything runs at 44.1 kHz.
- Linear response. A 6-second exponential sine sweep, 10 Hz – 22 kHz, into the analog filter;
the impulse response is recovered by deconvolution with an amplitude-modulated inverse, then time-
windowed to drop the harmonic-distortion responses and keep the linear part. Compared against the
digital model driven by a low-level impulse (below the ~26 mV where the
tanhstages stay linear). - Nonlinear response. An analog sine and a sawtooth, 12 V peak-to-peak, fundamental 500 Hz, cutoff ≈ 3.7 kHz (70% knob), resonance 0 — recorded, then replayed into the digital model.
The digital model is D'Angelo & Välimäki's analog model implemented two ways: a "trivial" implicit- midpoint version and an antialiased version using the antiderivative method.
The result
"Comparison of measurements of the analog and digital filters show that the digital model is accurate within a few dB in the linear regime and has very similar behavior in the nonlinear regime in terms of distortion." In the nonlinear plots the analog filter produces odd harmonic distortion; the low-level even harmonics are attributed to input noise and to the transistors saturating slightly asymmetrically, and are set aside as negligible. Without antialiasing, the nonlinear output carries aliased components that the antiderivative method suppresses.
Three findings the measurement produced that no analysis would have
- The front panel lies about its own numbers. "The labels on the synthesizer's cutoff frequency knob do not map directly to the measured cutoff frequency", so the authors had to measure the −12 dB point across knob positions and fit an exponential to recover the real mapping.
- Resonance has no scale at all. The knob position maps to no published value, so the paper reports resonance in percent of knob travel and fits its own linear mapping to the model's feedback coefficient k. 0% and 10% both give k = 0; at 70% the filter starts behaving nonlinearly and at about 80% it self-oscillates, after which "the measurement becomes illegible due to noise."
- There is an undocumented attenuator in front of the filter. It only became evident after the high-level runs, and it had to be added to the digital model by ear — "the attenuation value was chosen empirically to match the analog measurements."
Those three are the page's real contribution to this spoke. The modelling literature argues about the circuit; the measurement ran into a control surface whose labels, scale and input stage are all undocumented, and two of the three fixes were empirical.
What it still does not settle
No listening test. The comparison is spectral throughout — frequency response and harmonic magnitude — so audible difference remains unmeasured, which is the half digital-filter-audibility and meyer-moran-adda-loop work and this paper does not. "Accurate within a few dB in the linear regime" is also not a null result: a few dB around a resonant peak is not nothing, and the paper draws no threshold.
Related
moog-ladder-nonlinear-digital · analog-vs-digital · analog-vs-digital-pedals · digital-filter-audibility · meyer-moran-adda-loop · synthesis