The wave digital filter (WDF) technique derives digital filters from analog prototypes that classically have been restricted to passive circuits with series/parallel topologies. Since most audio circuits contain active elements (e.g., op-amps) and complex topologies, WDFs have only had limited use in virtual analog modeling. In this paper, we extend the WDF approach to accommodate the unbounded class of non-series/parallel junctions which may absorb linear multiports. We present four modified-nodal-analysis-based scattering matrix derivations for these junctions, using parametric waves with voltage, power, and current waves as particular cases. Three derivations afford implementations whose cost in multiplies are lower than multiplying by the scattering matrix. Negative port resistances may be needed in WDF modeling of active circuits, restricting the WDF to voltage or current waves. We propose two techniques for localizing this restriction. Case studies on the Baxandall tone circuit and a ``Frequency Booster'' guitar pedal demonstrate the proposed techniques in action.

In this paper, an existing approach for modeling and efficiently implementing arbitrary reciprocal connection networks using wave digital (WD) scattering junctions based on voltage waves is extended to be used in a broader class of WD filters (WDFs) based on different kinds of waves. A generalized wave definition which includes traditional voltage waves, current waves, and power-normalized waves as particular cases is employed. Closed-form formulas for computing the scattering matrices of the junctions are provided. Moreover, the approach is also extended to the family of Biparametric WDFs, which have been recently introduced in the literature.

We extend the Wave Digital Filter (WDF) approach to simulate reference circuits that involve operational amplifiers (op-amps). We handle both nullor-based ideal op-amp models and controlled-source-based linear op-amp macromodels in circuits with arbitrary topologies using recent derivations for complicated scattering matrices. The presented methods greatly increase the class of appropriate circuits for virtual analog modeling, and readily extend to circuits with any number of op-amps. Although op-amps are essential to many circuits and deviations from ideal can be important, previous WDF research applies only to the limited case of circuits with ideal op-amps, in differential amplifier topology, with no global feedback.

The magnitude of the Discrete Fourier Transform (DFT) of a discrete-time signal has a limited frequency definition. Quadratic interpolation over the three DFT samples surrounding magnitude peaks improves the estimation of parameters (frequency and amplitude) of resolved sinusoids beyond that limit. Interpolating on a rescaled magnitude spectrum using a logarithmic scale has been shown to improve those estimates. In this article, we show how to heuristically tune a power scaling parameter to outperform linear and logarithmic scaling at an equivalent computational cost. Although this power scaling factor is computed heuristically rather than analytically, it is shown to depend in a structured way on window parameters. Invariance properties of this family of estimators are studied and the existence of a bias due to noise is shown. Comparing to two state-of-the-art estimators, we show that an optimized power scaling has a lower systematic bias and lower mean-squared-error in noisy conditions for ten out of twelve common windowing functions.

In this design study, we introduce a novel class of digital audio effects that extend the recently introduced modal processor approach to artificial reverberation and effects processing. These pitch and distortion processing effects mimic the design and sonics of a classic additive-synthesis-based electromechanical musical instrument, the Hammond tonewheel organ. As a reverb effect, the modal processor simulates a room response as the sum of resonant filter responses. This architecture provides precise, interactive control over the frequency, damping, and complex amplitude of each mode. Into this framework, we introduce two types of processing effects: pitch effects inspired by the Hammond organ’s equal tempered “tonewheels”, “drawbar” tone controls, vibrato/chorus circuit, and distortion effects inspired by the pseudo-sinusoidal shape of its tonewheels and electromagnetic pickup distortion. The result is an effects processor that imprints the Hammond organ’s sonics onto any audio input.

The Wave Digital Filter approach can be used to create computational models of lumped reference systems, including rectilinear mechanical, rotational mechanical, acoustical, and electronic systems. When they are applicable, Wave Digital Filters enjoy properties including modularity, accuracy, and guaranteed incremental passivity that make them attractive in the context of musical instrument and audio effect simulation. However, the class of reference systems that can be modeled with Wave Digital Filters has historically been restricted to systems with simple topologies (which can be decomposed entirely into series and parallel connections) and which contain only a single “nonadaptable” element (e.g., a diode, ideal source, or switch). This talk details recent Wave Digital Filter advances from Stanford University's Center for Computer Research in Music and Acoustics (CCRMA), which broaden the applicability of Wave Digital Filters to reference systems with any topology and an arbitrary number of nonlinearities or other nonadaptable elements. These advances have enabled many new and previously intractable musical circuit simulations at CCRMA, including active tone stages and transistor/diode/feedback clipping from guitar distortion pedals, the electromechanical Hammond organ vibrato/chorus system, guitar tube pre-amplifiers and tone stacks, circuits involving operational amplifiers, drum machine circuits, and transistor amplifiers.