Modal representations—decomposing the resonances of objects into their vibrational modes has historically been a powerful tool for studying and synthesizing the sounds of physical objects, but it also provides a flexible framework for abstract sound synthesis. In this paper, we demonstrate a variety of musically relevant ways to modify the model upon resynthesis employing a carillon model as a case study. Using a set of audio recordings of the sixty bells of the Robert and Ann Lurie Carillon recorded at the University of Michigan, we present a modal analysis of these recordings, in which we decompose the sound of each bell into a sum of decaying sinusoids. Each sinusoid is characterized by a modal frequency, exponential decay rate, and initial complex amplitude. This analysis yields insight into the timbre of each individual bell as well as the entire carillon as an ensemble. It also yields a powerful parametric synthesis model for reproducing bell sounds and bell-based audio effects.

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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.

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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.

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The recently proposed antiderivative antialiasing (ADAA) technique for stateful systems involves two key features: 1) replacing a nonlinearity in a physical model or virtual analog simulation with an antialiased nonlinear system involving antiderivatives of the nonlinearity and time delays and 2) introducing a digital filter in cascade with each original delay in the system. Both of these features introduce the same delay, which is compensated by adjusting the sampling period. The result is a simulation with reduced aliasing distortion. In this paper, we study ADAA using equivalent circuits, answering the question: “Which electrical circuit, discretized using the bilinear transform, yields the ADAA system?” This gives us a new way of looking at the stability of ADAA and how introducing extra filtering distorts a system’s response. We focus on the Wave Digital Filter (WDF) version of this technique.

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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.

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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.

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