Download Discretization of the '59 Fender Bassman Tone Stack The market for digital modeling guitar amplifiers requires that the digital models behave like the physical prototypes. A component of the iconic Fender Bassman guitar amplifier, the tone stack circuit, filters the sound of the electric guitar in a unique and complex way. The controls are not orthogonal, resulting in complicated filter coefficient trajectories as the controls are varied. Because of its electrical simplicity, the tone stack is analyzed symbolically in this work, and digital filter coefficients are derived in closed form. Adhering to the technique of virtual analog, this procedure results in a filter that responds to user controls in exactly the same way as the analog prototype. The general expressions for the continuous-time and discrete-time filter coefficients are given, and the frequency responses are compared for the component values of the Fender ’59 Bassman. These expressions are useful implementation and verification of implementations such as the wave digital filter.
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.