Download Uniform Noise Sequences for Nonlinear System Identification Noise-based nonlinear system identification techniques using Hammerstein and Wiener forms have found wide application in biological system modeling, and been applied to modeling nonlinear audio processors such as the ring modulator. These methods apply noise to the system, and project the system output onto a set of orthogonal polynomials to reveal parameters of the model. Though Gaussian sequences are invariably used to drive the unknown system, it seems clear that the statistics of the input will affect the model estimate. Motivated by the limited input and output ranges supported by analog systems, in this work, the use of an input noise sequence having a uniform distribution is explored. In addition, an error measure indicating harmonic distortion modeling accuracy is introduced. Simulation results identifying Hammerstein and Wiener systems show that the uniform and Gaussian distributions perform differently, with the uniform distribution generally producing more accurate harmonic responses. Finally, uniform noise and Gaussian noise are used to model a saturating low-pass circuit similar to that of the Tube Screamer, with the uniform distribution providing a modest improvement in noise response error.
Download Design principles for lumped model discretisation using Möbius transforms Computational modelling of audio systems commonly involves discretising lumped models. The properties of common discretisation schemes are typically derived through analysis of how the imaginary axis on the Laplace-transform s-plane maps onto the Ztransform z-plane and the implied stability regions. This analysis ignores some important considerations regarding the mapping of individual poles, in particular the case of highly-damped poles. In this paper, we analyse the properties of an extended class of discretisations based on Möbius transforms, both as mappings and discretisation schemes. We analyse and extend the concept of frequency warping, well-known in the context of the bilinear transform, and we characterise the relationship between the damping and frequencies of poles in the s- and z-planes. We present and analyse several design criteria (damping monotonicity, stability) corresponding to desirable properties of the discretised system. Satisfying these criteria involves selecting appropriate transforms based on the pole structure of the system on the s-plane. These theoretical developments are finally illustrated on a diode clipper nonlinear model.
Download A Computational Model of the Hammond Organ Vibrato/Chorus using Wave Digital Filters We present a computational model of the Hammond tonewheel organ vibrato/chorus, a musical audio effect comprising an LC ladder circuit and an electromechanical scanner. We model the LC ladder using the Wave Digital Filter (WDF) formalism, and introduce a new approach to resolving multiple nonadaptable linear elements at the root of a WDF tree. Additionally we formalize how to apply the well-known warped Bilinear Transform to WDF discretization of capacitors and inductors and review WDF polarity inverters. To model the scanner we propose a simplified and physically-informed approach. We discuss the time- and frequency-domain behavior of the model, emphasizing the spectral properties of interpolation between the taps of the LC ladder.