Download WDF Modeling of a Korg MS-50 Based Non-linear Diode Bridge VCF
The voltage-controlled low-pass filter of the Korg MS-50 synthesizer is built around a non-linear diode bridge as the cutoff frequency control element, which greatly contributes to the sound of this vintage synthesizer. In this paper, we introduce the overall filter circuitry and give an in-depth analysis of this diode bridge. It is further shown how to turn the small signal equivalence circuit of the bridge into the necessary two-resistor configuration to uncover the underlying Sallen-Key structure. In a second step, recent advances in the field of WDFs are used to turn a simplified version of the circuit into a virtual-analog model. This model is then examined both in the small-signal linear domain as well as in the non-linear region with inputs of different amplitudes and frequencies to characterize the behavior of such diode bridges as cutoff frequency control elements.
Download Resolving Grouped Nonlinearities in Wave Digital Filters using Iterative Techniques
In this paper, iterative zero-finding techniques are proposed to resolve groups of nonlinearities occurring in Wave Digital Filters. Two variants of Newton’s method are proposed and their suitability towards solving the grouped nonlinearities is analyzed. The feasibility of the approach with implications for WDFs containing multiple nonlinearities is demonstrated via case studies investigating the mathematical properties and numerical performance of reference circuits containing diodes and transistors; asymmetric and symmetric diode clippers and a common emitter amplifier.
Download Modeling and Extending the Rca Mark Ii Sound Effects Filter
We have analyzed the Sound Effects Filter from the one-of-a-kind RCA Mark II sound synthesizer and modeled it as a Wave Digital Filter using the Faust language, to make this once exclusive device widely available. By studying the original schematics and measurements of the device, we discovered several circuit modifications. Building on these, we proposed a number of extensions to the circuit which increase its usefulness in music production.
Download Moog Ladder Filter Generalizations Based on State Variable Filters
We propose a new style of continuous-time filter design composed of a cascade of 2nd-order state variable filters (SVFs) and a global feedback path. This family of filters is parameterized by the SVF cutoff frequencies and resonances, as well as the global feedback amount. For the case of two identical SVFs in cascade and a specific value of the SVF resonance, the proposed design reduces to the well-known Moog ladder filter. For another resonance value, it approximates the Octave CAT filter. The resonance parameter can be used to create new filters as well. We study the pole loci and transfer functions of the SVF building block and entire filter. We focus in particular on the effect of the proposed parameterization on important aspects of the filter’s response, including the passband gain and cutoff frequency error. We also present the first in-depth study of the Octave CAT filter circuit.
Download Energy-Preserving Time-Varying Schroeder Allpass Filters
In artificial reverb algorithms, gains are commonly varied over time to break up temporal patterns, improving quality. We propose a family of novel Schroeder-style allpass filters that are energypreserving under arbitrary, continuous changes of their gains over time. All of them are canonic in delays, and some are also canonic in multiplies. This yields several structures that are novel even in the time-invariant case. Special cases for cascading and nesting these structures with a reduced number of multipliers are shown as well. The proposed structures should be useful in artificial reverb applications and other time-varying audio effects based on allpass filters, especially where allpass filters are embedded in feedback loops and stability may be an issue.
Download Time-Varying Filter Stability and State Matrix Products
We show a new sufficient criterion for time-varying digital filter stability: that the matrix norm of the product of state matrices over a certain finite number of time steps is bounded by 1. This extends Laroche’s Criterion 1, which only considered one time step, while hinting at extensions to two time steps. Further extending these results, we also show that there is no intrinsic requirement that filter coefficients be frozen over any time scale, and extend to any dimension a helpful theorem that allows us to avoid explicitly performing eigen- or singular value decompositions in studying the matrix norm. We give a number of case studies on filters known to be time-varying stable, that cannot be proven time-varying stable with the original criterion, where the new criterion succeeds.