Download Accurate Reverberation Time Control in Feedback Delay Networks The reverberation time is one of the most prominent acoustical qualities of a physical room. Therefore, it is crucial that artificial reverberation algorithms match a specified target reverberation time accurately. In feedback delay networks, a popular framework for modeling room acoustics, the reverberation time is determined by combining delay and attenuation filters such that the frequencydependent attenuation response is proportional to the delay length and by this complying to a global attenuation-per-second. However, only few details are available on the attenuation filter design as the approximation errors of the filter design are often regarded negligible. In this work, we demonstrate that the error of the filter approximation propagates in a non-linear fashion to the resulting reverberation time possibly causing large deviation from the specified target. For the special case of a proportional graphic equalizer, we propose a non-linear least squares solution and demonstrate the improved accuracy with a Monte Carlo simulation.
Download Real-Time Modal Synthesis of Nonlinearly Interconnected Networks Modal methods are a long-established approach to physical modeling sound synthesis. Projecting the equation of motion of a linear, time-invariant system onto a basis of eigenfunctions yields a set of independent forced, lossy oscillators, which may be simulated efficiently and accurately by means of standard time-stepping methods. Extensions of modal techniques to nonlinear problems are possible, though often requiring the solution of densely coupled nonlinear time-dependent equations. Here, an application of recent results in numerical simulation design is employed, in which the nonlinear energy is first quadratised via a convenient auxiliary variable. The resulting equations may be updated in time explicitly, thus avoiding the need for expensive iterative solvers, dense linear system solutions, or matrix inversions. The case of a network of interconnected distributed elements is detailed, along with a real-time implementation as an audio plugin.
Download Quadratic Spline Approximation of the Contact Potential for Real-Time Simulation of Lumped Collisions in Musical Instruments Collisions are an integral part of the sound production mechanism in a wide variety of musical instruments. In physics-based realtime simulation of such nonlinear phenomena, challenges centred around efficient and accurate root-finding arise. Nonlinearly implicit schemes are normally ill-suited for real-time simulation as they rely on iterative solvers for root-solving. Explicit schemes overcome this issue at the cost of a slightly larger error for a given sample rate. In this paper, for the case of lumped collisions, an alternate approach is proposed by approximating the contact potential curve. The approximation is described, and is shown to lead to a non-iterative update for an energy-stable nonlinearly implicit scheme. The method is first tested on single mass-barrier collision simulations, and then employed in conjunction with a modal string model to simulate hammer-string and slide-string interaction. Results are discussed in comparison with existing approaches, and real-time feasibility is demonstrated.
Download Real-Time Guitar Synthesis The synthesis of guitar tones was one of the first uses of physical modeling synthesis, and many approaches (notably digital waveguides) have been employed. The dynamics of the string under playing conditions is complex, and includes nonlinearities, both inherent to the string itself, and due to various collisions with the fretboard, frets and a stopping finger. All lead to important perceptual effects, including pitch glides, rattling against frets, and the ability to play on the harmonics. Numerical simulation of these simultaneous strong nonlinearities is challenging, but recent advances in algorithm design due to invariant energy quadratisation and scalar auxiliary variable methods allow for very efficient and provably numerically stable simulation. A new design is presented here that does not employ costly iterative methods such as the Newton-Raphson method, and for which required linear system solutions are small. As such, this method is suitable for real-time implementation. Simulation and timing results are presented.
Download Ray Acoustics Using Computer Graphics Technology The modeling of room acoustics and simulation of sound wave propagation remain a difficult and computationally expensive task. Two main techniques have evolved, with one focusing on a real physical - wave-oriented - sound propagation, while the other approximates sound waves as rays using raytracing techniques. Due to many advances in computer science, and especially computer graphics over the last decade, interactive 3D sound simulations for complex and dynamic environments are within reach. In this paper we analyze sound propagation in terms of acoustic energy and explore the possibilities to map these concepts to radiometry and graphics rendering equations. Although we concentrate on ray-based techniques, we also partially consider wavebased sound propagation effects. The implemented system exploits modern graphics hardware and rendering techniques and is able to efficiently simulate 3D room acoustics, as well as to measure simplified personal HRTFs through acoustic raytracing.
Download Real-Time and Efficient Algorithms for Frequency Warping Based on Local Approximations of Warping Operators Frequency warping is a modifier that acts on sound signals by remapping the frequency axis. Thus, the spectral content of the original sound is displaced to other frequencies. At the same time, the phase relationship among the signal components is altered, nonlinearly with respect to frequency. While this effect is interesting and has several applications, including in the synthesis by physical models, its use has been so far limited by the lack of an accurate and flexible real-time algorithm. In this paper we present methods for frequency warping that are based on local approximations of the warping operators and allow for real-time implementation. Filter bank structures are derived that allow for efficient realization of the approximate technique. An analysis of the error is also presented, which shows that both numerical and perceptual errors are within acceptable limits. Furthermore, the approximate implementation allows for a larger variety of warping maps than that achieved by the classical (non-causal) first-order allpass cascade implementation.
Download Alias-free Virtual Analog Oscillators Using a Feedback Delay Loop The rich spectra of classic waveforms (sawtooth, square and triangular) are obtained by discontinuities in the waveforms or their derivatives. At the same time, the discontinuities lead to aliasing when the waveforms are digitally generated. To remove or reduce the aliasing, researchers have proposed various methods, mostly based on limiting bandwidth or smoothing the waveforms. This paper introduces a new approach to generate the virtual analog oscillators with no aliasing. The approach relies on generating an impulse train using a feedback delay loop, often used for the physical modeling of musical instruments. Classic waveforms are then derived from the impulse train with a leaky integrator. Although the output generated by this method is not exactly periodic, it perceptually sounds harmonic. While additional processing is required for time-varying pitch shifting, resulting in some high-frequency attenuation when the pitch changes, the proposed method is computationally more efficient than other algorithms and the high-frequency attenuation can be also adjusted.
Download Automatic calibration and equalization of a line array system This paper presents an automated Public Address processing unit, using delay and magnitude response adjustment. The aim is to achieve a flat frequency response and delay adjustment between different physically-placed speakers at the measuring point, which is nowadays usually made manually by the sound technician. The adjustment is obtained using three signal processing operations to the audio signal: time delay adjustment, crossover filtering, and graphic equalization. The automation is in the calculation of different parameter sets: estimation of the time delay, the selection of a suitable crossover frequency, and calculation of the gains for a third-octave graphic equalizer. These automatic methods reduce time and effort in the calibration of line-array PA systems, since only three sine sweeps must be played through the sound system. Measurements have been conducted in an anechoic chamber using a 1:10 scale model of a line array system to verify the functioning of the automatic calibration and equalization methods.
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 Flexible software framework for modal synthesis Modal synthesis is an important area of physical modeling whose exploration in the past has been held back by a large number of control parameters, the scarcity of generalpurpose design tools and the difficulty of obtaining the computational power required for real-time synthesis. This paper presents an overview of a flexible software framework facilitating the design and control of instruments based on modal synthesis. The framework is designed as a hierarchy of polymorphic synthesis objects, representing modal structures of various complexity. As a method of generalizing all interactions among the elements of a modal system, an abstract notion of energy is introduced, and a set of energy transfer functions is provided. Such abstraction leads to a design where the dynamics of interactions can be largely separated from the specifics of particular modal structures, yielding an easily configurable and expandable system. A real-time version of the framework has been implemented as a set of C++ classes along with an integrating shell and a GUI, and is currently being used to design and play modal instruments, as well as to survey fundamental properties of various modal algorithms.