Download Distribution Derivative Method for Generalised Sinusoid with Complex Amplitude Modulation
The most common sinusoidal models for non-stationary analysis represent either complex amplitude modulated exponentials with exponential damping (cPACED) or log-amplitude/frequency modulated exponentials (generalised sinusoids), by far the most commonly used modulation function being polynomials for both signal families. Attempts to tackle a hybrid sinusoidal model, i.e. a generalised sinusoid with complex amplitude modulation were relying on approximations and iterative improvement due to absence of a tractable analytical expression for their Fourier Transform. In this work a simple, direct solution for the aforementioned model is presented.
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 Wave Digital Filter Adaptors for Arbitrary Topologies and Multiport Linear Elements
We present a Modified-Nodal-Analysis-derived method for developing Wave Digital Filter (WDF) adaptors corresponding to complicated (non-series/parallel) topologies that may include multiport linear elements (e.g. controlled sources and transformers). A second method resolves noncomputable (non-tree-like) arrangements of series/parallel adaptors. As with the familiar 3-port series and parallel adaptors, one port of each derived adaptor may be rendered reflection-free, making it acceptable for inclusion in a standard WDF tree. With these techniques, the class of acceptable reference circuits for WDF modeling is greatly expanded. This is demonstrated by case studies on circuits which were previously intractable with WDF methods: the Bassman tone stack and Tube Screamer tone/volume stage.
Download Resolving Wave Digital Filters with Multiple/Multiport Nonlinearities
We present a novel framework for developing Wave Digital Filter (WDF) models from reference circuits with multiple/multiport nonlinearities. Collecting all nonlinearities into a vector at the root of a WDF tree bypasses the traditional WDF limitation to a single nonlinearity. The resulting system has a complicated scattering relationship between the nonlinearity ports and the ports of the rest of the (linear) circuit, which can be solved by a Modified-NodalAnalysis-derived method. For computability reasons, the scattering and vector nonlinearity must be solved jointly; we suggest a derivative of the K-method. This novel framework significantly expands the class of appropriate WDF reference circuits. A case study on a clipping stage from the Big Muff Pi distortion pedal involves both a transistor and a diode pair. Since it is intractable with standard WDF methods, its successful simulation demonstrates the usefulness of the novel framework.
Download Simulations of Nonlinear Plate Dynamics: An Accurate and Efficient Modal Algorithm
This paper presents simulations of nonlinear plate vibrations in relation to sound synthesis of gongs and cymbals. The von Kármán equations are shown and then solved in terms of the modes of the associated linear system. The modal equations obtained constitute a system of nonlinearly coupled Ordinary Differential Equations which are completely general as long as the modes of the system are known. A simple second-order time-stepping integration scheme yields an explicit resolution algorithm with a natural parallel structure. Examples are provided and the results discussed.
Download An Algorithm for a Valved Brass Instrument Synthesis Environment using Finite-Difference Time-Domain Methods with Performance Optimisation
This paper presents a physical modelling sound synthesis environment for the production of valved brass instrument sounds. The governing equations of the system are solved using finite-difference time-domain (FDTD) methods and the environment is implemented in the C programming language. Users of the environment can create their own custom instruments and are able to control player parameters such as lip frequency, mouth pressure and valve openings through the use of instrument and score files. The algorithm for sound synthesis is presented in detail along with a discussion of optimisation methods used to reduce run time. Binaries for the environment are available for download online for multiple platforms.
Download Downmix compatible conversion from mono to stereo in time- and frequency-domain
Even in a time of surround and 3D sound, many tracks and recordings are still only available in mono or it is not feasible to record a source with multiple microphones for several reasons. In these cases, a pseudo stereo conversion of mono signals can be a useful preprocessing step and/or an enhancing audio effect. The conversion proposed in this paper is designed to deliver a neutral sounding stereo image by avoiding timbral coloration or reverberation. Additionally, the resulting stereo signal is downmix-compatible and allows to revert to the original mono signal by a simple summation of the left and right channels. Several configuration parameters are shown to control the stereo panorama. The algorithm can be implemented in time-domain or also in the frequency-domain with additional features, like center focusing.
Download Development of an outdoor auralisation prototype with 3D sound reproduction
Auralisation of outdoor sound has a strong potential for demonstrating the impact of different community noise scenarios. We describe here the development of an auralisation tool for outdoor noise such as traffic or industry. The tool calculates the sound propagation from source to listener using the Nord2000 model, and represents the sound field at the listener’s position using spherical harmonics. Because of this spherical harmonics approach, the sound may be reproduced in various formats, such as headphones, stereo, or surround. Dynamic reproduction in headphones according to the listener’s head orientation is also possible through the use of head tracking.
Download Swing Ratio Estimation
Swing is a typical long-short rhythmical pattern that is mostly present in jazz music. In this article, we propose an algorithm to automatically estimate how much a track, a frame of a track, is swinging. We denote this by swing ratio. The algorithm we propose is based on the analysis of the auto-correlation of the onset energy function of the audio signal and a simple set of rules. For the purpose of the evaluation of this algorithm, we propose and share the “GTZAN-rhythm” test-set, which is an extension of a well-known test-set by adding annotations of the whole rhythmical structure (downbeat, beat and eight-note positions). We test our algorithm for two tasks: detecting tracks with or without swing, and estimating the amount of swing. Our algorithm achieves 91% mean recall. Finally we use our annotations to study the relationship between the swing ratio and the tempo (study the common belief that swing ratio decreases linearly with the tempo) and the musicians. How much and how to swing is never written on scores, and is therefore something to be learned by the jazzstudents mostly by listening. Our algorithm could be useful for jazz student who wants to learn what is swing.
Download Wavelet scattering along the pitch spiral
We present a new representation of harmonic sounds that linearizes the dynamics of pitch and spectral envelope, while remaining stable to deformations in the time-frequency plane. It is an instance of the scattering transform, a generic operator which cascades wavelet convolutions and modulus nonlinearities. It is derived from the pitch spiral, in that convolutions are successively performed in time, log-frequency, and octave index. We give a closed-form approximation of spiral scattering coefficients for a nonstationary generalization of the harmonic source-filter model.