Download Energy Shaping of a Softening Duffing Oscillator Using the Formalism of Port-Hamiltonian Systems This work takes place in the context of the development of an active control of instruments with geometrical nonlinearities. The study focuses on Chinese opera gongs that display a characteristic pitch glide in normal playing conditions. In the case of the xiaoluo gong, the fundamental mode of the instrument presents a softening behaviour (frequency glides upward when the amplitude decreases). Controlling the pitch glide requires a nonlinear model of the structure, which can be partially identified with experimental techniques that rely on the formalism of nonlinear normal modes. The fundamental nonlinear mode has been previously experimentally identified as a softening Duffing oscillator. This paper aims at performing a simulation of the control of the oscillator’s pitch glide. For this purpose, the study focuses on a single-degree-offreedom nonlinear mode described by a softening Duffing equation. This Duffing oscillator energy proves to be ill-posed - in particular, the energy becomes negative for large amplitudes of vibration, which is physically inconsistent. Then, the first step of the present study consists in redefining a new energetically well-posed model. In a second part, guaranteed-passive simulations using port-Hamiltonian formalism confirm that the new system is physically and energetically correct compared to the Duffing model. Third, the model is used for control issues in order to modify the softening or hardening behaviour of the fundamental pitch glide. Results are presented and prove the method to be relevant. Perspectives for experimental applications are finally exposed in the last section of the paper.
Download On Iterative Solutions for Numerical Collision Models Nonlinear interactions between different parts of musical instruments present several challenges regarding the formulation of reliable and efficient numerical sound synthesis models. This paper focuses on a numerical collision model that incorporates impact damping. The proposed energy-based approach involves an iterative solver for the solution of the nonlinear system equations. In order to ensure the efficiency of the presented algorithm a bound is derived for the maximum number of iterations required for convergence. Numerical results demonstrate energy conservation as well as convergence within a small number of iterations, which is usually much lower than the predicted bound. Finally, an application to music acoustics, involving a clarinet simulation, shows that including a loss mechanism during collisions may have a significant effect on sound production.
Download A Numerical Scheme for Various Nonlinear Forces, Including Collisions, Which Does Not Require an Iterative Root Finder Nonlinear forces are ubiquitous in physical systems, and of prominent importance in musical acoustics. Though many models exist to describe such forces, in most cases the associated numerical schemes rely on iterative root finding methods, such as NewtonRaphson or gradient descent, which are computationally expensive and which therefore could represent a computational bottleneck. In this paper, a model for a large class of nonlinear forces is presented, and a novel family of energy-conserving finite difference schemes given. The schemes only require the evaluation of the roots of a quadratic function. A few applications in the lumped case are shown, and the robustness and accuracy of the scheme tested.
Download Trajectory Anti-aliasing on Guaranteed-passive Simulation of Nonlinear Physical Systems This article is concerned with the accurate simulation of passive nonlinear dynamical systems with a particular attention paid on aliasing reduction in the pass-band. The approach is based on the combination of Port-Hamiltonian Systems, continuous-time statespace trajectories reconstruction and exact continuous-time antialiasing filter realization. The proposed framework is applied on a nonlinear LC oscillator circuit to study the effectiveness of the method.
Download The Quest for the Best Graphic Equalizer The design of graphic equalizers has been investigated for decades, but only recently fitting the magnitude response closely enough to the control points has become possible. This paper reviews the development of graphic equalizer design and discusses how to define the target response. Furthermore, it investigates how to find the hardest target gain settings, the definition of the bandwidth of band filters, the estimation of the interaction between the bands, and how the number of iterations improves the design. The main focus is on a recent design principle for the cascade graphic equalizer. This paper extends the design method for the case of third-octave bands, showing how to choose the parameters to obtain good accuracy. The main advantages of the proposed approach are that it keeps the approximation error below 1 dB using only a single second-order IIR filter section per band, and that its design is fast. The remaining challenge is to simplify the design phase so that sufficient accuracy can be obtained without iterations.
Download Audio Processing Chain Recommendation In sound production, engineers cascade processing modules at various points in a mix to apply audio effects to channels and busses. Previous studies have investigated the automation of parameter settings based on external semantic cues. In this study, we provide an analysis of the ways in which participants apply full processing chains to musical audio. We identify trends in audio effect usage as a function of instrument type and descriptive terms, and show that processing chain usage acts as an effective way of organising timbral adjectives in low-dimensional space. Finally, we present a model for full processing chain recommendation using a Markov Chain and show that the system’s outputs are highly correlated with a dataset of user-generated processing chains.
Download Investigation of a Drum Controlled Cross-adaptive Audio Effect for Live Performance Electronic music often uses dynamic and synchronized digital audio effects that cannot easily be recreated in live performances. Cross-adaptive effects provide a simple solution to such problems since they can use multiple feature inputs to control dynamic variables in real time. We propose a generic scheme for cross-adaptive effects where onset detection on a drum track dynamically triggers effects on other tracks. This allows a percussionist to orchestrate effects across multiple instruments during performance. We describe the general structure that includes an onset detection and feature extraction algorithm, envelope and LFO synchronization, and an interface that enables the user to associate different effects to be triggered depending on the cue from the percussionist. Subjective evaluation is performed based on use in live performance. Implications on music composition and performance are also discussed. Keywords: Cross-adaptive digital audio effects, live processing, real-time control, Csound.
Download Real-time Pitch Tracking in Audio Signals with the Extended Complex Kalman Filter The Kalman filter is a well-known tool used extensively in robotics, navigation, speech enhancement and finance. In this paper, we propose a novel pitch follower based on the Extended Complex Kalman Filter (ECKF). An advantage of this pitch follower is that it operates on a sample-by-sample basis, unlike other block-based algorithms that are most commonly used in pitch estimation. Thus, it estimates sample-synchronous fundamental frequency (assumed to be the perceived pitch), which makes it ideal for real-time implementation. Simultaneously, the ECKF also tracks the amplitude envelope of the input audio signal. Finally, we test our ECKF pitch detector on a number of cello and double bass recordings played with various ornaments, such as vibrato, portamento and trill, and compare its result with the well-known YIN estimator, to conclude the effectiveness of our algorithm.
Download Efficient Anti-aliasing of a Complex Polygonal Oscillator Digital oscillators with discontinuities in their time domain signal derivative suffer from an increased noise floor due to the unbound spectrum generated by these discontinuities. Common antialiasing schemes that aim to suppress the unwanted fold-back of higher frequencies can become computationally expensive, as they often involve repeated sample rate manipulation and filtering. In this paper, the authors present an effective approach to applying the four-point polyBLAMP method to the continuous order polygonal oscillator by deriving a closed form expression for the derivative jumps which is only valid at the discontinuities. Compared to the traditional oversampling approach, the resulting SNR improvements of 20 dB correspond to 2–4× oversampling at 25× lower computational complexity, all while offering a higher suppression of aliasing artifacts in the audible range.
Download Modeling Circuits with Operational Transconductance Amplifiers Using Wave Digital Filters In this paper, we show how to expand the class of audio circuits that can be modeled using Wave Digital Filters (WDFs) to those involving operational transconductance amplifiers (OTAs). Two types of behavioral OTA models are presented and both are shown to be compatible with the WDF approach to circuit modeling. As a case study, an envelope filter guitar effect based around OTAs is modeled using WDFs. The modeling results are shown to be accurate when to compared to state of the art circuit simulation methods.