Download Robust Design of Very High-Order Allpass Dispersion Filters
A nonparametric allpass filter design method is presented for matching a desired group delay as a function of frequency. The technique is useful in physical modeling synthesis of musical instruments and emulation of audio effects devices exhibiting dispersive wave propagation. While current group delay filter design methods suffer from numerical difficulties except at low filter orders, the technique presented here is numerically robust, producing an allpass filter in cascaded biquad form, and with the filter poles following a smooth loop within the unit circle. The technique was inspired by the observation that a pole-zero pair arranged in allpass form contributes exactly 2π radians to the integral of group delay around the unit circle, regardless of the (stable) pole location. To match a given group delay characteristic, the method divides the frequency axis into sections containing 2π total area under the desired group-delay curve, and assigns a polezero allpass pair to each. In this way, the method incorporates an order selection technique, and by adding a pure delay to the desired group delay, allows the trading of increased filter order for improved fit to the frequency-dependent group delay. Design examples are given for modeling the group delay of a dispersive string (such as a piano string), and a dispersive spring, such as in a spring reverberator.
Download A Stable Acoustic Impedance Model of the Clarinet using Digital Waveguides
Digital waveguide (DW) modeling techniques are typically associated with a traveling-wave decomposition of wave variables and a “reflection function” approach to simulating acoustic systems. As well, it is often assumed that inputs and outputs to/from these systems must be formulated in terms of traveling-wave variables. In this paper, we provide a tutorial review of DW modeling of acoustic structures to show that they can easily accommodate physical input and output variables. Under certain constraints, these formulations reduce to simple “Schroeder reverb-like” computational structures. We also present a stable single-reed filter model that allows an explicit solution at the reed / air column junction. A clarinet-like system is created by combining the reed filter with a DW impedance model of a cylindrical air column.
Download Some Physical Audio Effects
This paper presents a survey of various audio effects that can be physically applied to a rigidly-terminated vibrating string. The string’s resonant behavior is described, and then the ability of active feedback control to “reprogram" the physics of the string is explained. Active damping, which is a direct result of applying classical control techniques, provides for an effect based on amplitude modulation (AM). Traditional electric guitar sustain techniques are elaborated upon, which suggest another approach for ensuring marginal stability of the system even in the presence of an arbitrary nonlinear and/or time-varying effect unit in the feedback loop. This approach involves placing a dynamic range limiter in the feedback loop and does not introduce significant harmonic distortion other than that due to the effect unit. The maximum RMS level of the system’s output can be easily bounded if reasonable conditions are met by the dynamic range limiter. Finally, nonlinear and time-varying feedback control loops are applied experimentally to artificially induce frequency modulation (FM) at a low rate and AM at a high rate. These effects can be interpreted musically as vibrato and as a sort of resonant ring modulation, respectively.
Download Simplified, Physically-Informed Models of Distortion and Overdrive Guitar Effects Pedals
This paper explores a computationally efficient, physically informed approach to design algorithms for emulating guitar distortion circuits. Two iconic effects pedals are studied: the “Distortion” pedal and the “Tube Screamer” or “Overdrive” pedal. The primary distortion mechanism in both pedals is a diode clipper with an embedded low-pass filter, and is shown to follow a nonlinear ordinary differential equation whose solution is computationally expensive for real-time use. In the proposed method, a simplified model, comprising the cascade of a conditioning filter, memoryless nonlinearity and equalization filter, is chosen for its computationally efficient, numerically robust properties. Often, the design of distortion algorithms involves tuning the parameters of this filter-distortion-filter model by ear to match the sound of a prototype circuit. Here, the filter transfer functions and memoryless nonlinearities are derived by analysis of the prototype circuit. Comparisons of the resulting algorithms to actual pedals show good agreement and demonstrate that the efficient algorithms presented reproduce the general character of the modeled pedals.
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 Simulating guitar distortion circuits using wave digital and nonlinear state-space formulations
This work extends previous research on numerical solution of nonlinear systems in musical acoustics to the realm of nonlinear musical circuits. Wave digital principles and nonlinear state-space simulators provide two alternative approaches explored in this work. These methods are used to simulate voltage amplification stages typically used in guitar distortion or amplifier circuits. Block level analysis of the entire circuit suggests a strategy based upon the nonlinear filter composition technique for connecting amplifier stages while accounting for the way these stages interact. Formulations are given for the bright switch, the diode clipper, a transistor amplifier, and a triode amplifier.
Download Low-order allpass Interpolated Delay Loops
This paper presents empirical and theoretical results for a delay line cascaded with a second-order allpass filter in a feedback loop. Though such a structure has been used for years to model stiff vibrating strings, the complete range of behavior of such a structure has not been fully described and analyzed. As shown in this paper, in addition to the desired behavior of providing a frequencydependent delay line length, other phenomena may occur, such as “beating” or “mode splitting.” Associated analysis simulation results are presented.
Download Recent CCRMA research in Digital Audio Synthesis, Processing and Effects
This extended abstract summarizes DAFx-related developments at CCRMA over the past year or so.
Download Spectral Dealy Filters with Feedback Delay Filters with Feedback and Time-Varying Coefficients
A recently introduced structure to implement a continuously smooth spectral delay, based on a cascade of first-order allpass filters and an equalizing filter, is described and the properties of this spectral delay filter are reviewed. A new amplitude envelope equalizing filter for the spectral delay filter is proposed and the properties of structures utilizing feedback and/or time-varying filter coefficients are discussed. In addition, the stability conditions for the feedback and the time-varying structures are derived. A spectral delay filter can be used for synthesizing chirp-like sounds or for modifying the timbre of arbitrary audio signals. Sound examples on the use of the spectral delay filters utilizing the structures discussed in this paper can be found at http://www.acoustics.hut. fi/publications/papers/dafx09-sdf/.
Download Pitch glide analysis and synthesis from Recorded Tones
Pitch glide is an important effect that occurs in nearly all plucked string instruments. In essence, large amplitude waves traveling on a string during the note onset increases the string tension above its nominal value, and therefore cause the pitch to temporarily increase. Measurements are presented showing an exponential relaxation of all the partial frequencies to their nominal values with a time-constant related to the decay rate of transverse waves propagating on the string. This exponential pitch trajectory is supported by a simple physical model in which the increased tension is somewhat counterbalanced by the increased length of the string. Finally, a method for synthesizing the plucked string via a novel hybrid digital waveguide-modal synthesis model is presented with implementation details for time-varying resonators.