Download Simulation of the Diode Limiter in Guitar Distortion Circuits by Numerical Solution of Ordinary Differential Equations The diode clipper circuit with an embedded low-pass filter lies at the heart of both diode clipping “Distortion” and “Overdrive” or “Tube Screamer” effects pedals. An accurate simulation of this circuit requires the solution of a nonlinear ordinary differential equation (ODE). Numerical methods with stiff stability – Backward Euler, Trapezoidal Rule, and second-order Backward Difference Formula – allow the use of relatively low sampling rates at the cost of accuracy and aliasing. However, these methods require iteration at each time step to solve a nonlinear equation, and the tradeoff for this complexity must be evaluated against simple explicit methods such as Forward Euler and fourth order Runge-Kutta, which require very high sampling rates for stability. This paper surveys and compares the basic ODE solvers as they apply to simulating circuits for audio processing. These methods are compared to a static nonlinearity with a pre-filter. It is found that implicit or semiimplicit solvers are preferred and that the filter/static nonlinearity approximation is often perceptually adequate.
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 Constrained Pole Optimization for Modal Reverberation The problem of designing a modal reverberator to match a measured room impulse response is considered. The modal reverberator architecture expresses a room impulse response as a parallel combination of resonant filters, with the pole locations determined by the room resonances and decay rates, and the zeros by the source and listener positions. Our method first estimates the pole positions in a frequency-domain process involving a series of constrained pole position optimizations in overlapping frequency bands. With the pole locations in hand, the zeros are fit to the measured impulse response using least squares. Example optimizations for a mediumsized room show a good match between the measured and modeled room responses.
Download The Sounds of the Avian Syrinx - are they Really Flute-Like? This research presents a model of the avian vocal tract, implemented using classical waveguide synthesis and numerical methods. The vocal organ of the songbird, the syrinx, has a unique topography of acoustic tubes (a trachea with a bifurcation at its base) making it a rather unique subject for waveguide synthesis. In the upper region of the two bifid bronchi lies a nonlinear vibrating membrane – the primary resonator in sound production. Unlike most reed musical instruments, the more significant displacement of the membrane is perpendicular to the directions of airflow, due to the Bernoulli effect. The model of the membrane displacement, and the resulting pressure through the constriction created by the membrane motion, is therefore derived beginning with the Bernoulli equation.
Download The Feathered Clarinet Reed In this research, a method previously In this research, a method previouslyapplied appliedtotoimprove improve a digital simulation of the avian syrinx is adapted to the geometry of the clarinet reed. The clarinet model is studied with particular attention to the case when the reed beats again the lay of the mouthpiece, closing off air flow to the bore once each period. In place of the standard reed table which gives steady-state volume flow as a function of constant pressure difference across the reed, a more realistic dynamic volume flow model is proposed. The differential equation governing volume flow dynamics is seen to have a singularity at the point of reed closure, where both the volume flow and reed channel area become zero. The feathered clarinet reed refers to the method, first used in the syrinx, to smooth or feather the volume flow cutoff in a closing valve. The feathered valve eliminates the singularity and reduces artifacts in the simulated clarinet output.
Download Synthesis of Sound Textures with Tonal Components Using Summary Statistics and All-Pole Residual Modeling The synthesis of sound textures, such as flowing water, crackling fire, an applauding crowd, is impeded by the lack of a quantitative definition. McDermott and Simoncelli proposed a perceptual source-filter model using summary statistics to create compelling synthesis results for non-tonal sound textures. However, the proposed method does not work well with tonal components. Comparing the residuals of tonal sound textures and non-tonal sound textures, we show the importance of residual modeling. We then propose a method using auto regressive modeling to reduce the amount of data needed for resynthesis and delineate a modified method for analyzing and synthesizing both tonal and non-tonal sound textures. Through user evaluation, we find that modeling the residuals increases the realism of tonal sound textures. The results suggest that the spectral content of the residuals has an important role in sound texture synthesis, filling the gap between filtered noise and sound textures as defined by McDermott and Simoncelli. Our proposed method opens possibilities of applying sound texture analysis to musical sounds such as rapidly bowed violins.