Scott A. Van Duyne

A passive nonlinear digital filter design which facilitates physics-based sound synthesis of highly nonlinear musical instruments

Recent work has led to highly efficient physics-based computational models of wave propagation in strings, acoustic tubes, membranes, plates, and rooms using the digital waveguide filter, the 2-D digital waveguide mesh, and the 3-D tetrahedral digital waveguide mesh, all of which are suitable for real-time musical synthesis applications. A simple first-order nonlinear filter structure derived from a passive nonlinear impedance circuit is described which extends the usefulness of these models, and which avoids the difficulties of energy conservation when memoryless nonlinearities are inserted in resonant feedback systems.

Apparatus and methods for synthesis of internal combustion engine vehicle sounds

Computer-implemented techniques are provided for synthesizing sounds of an internal combustion engine vehicle using a physical model of the vehicle. In general terms, the method includes independently generating and/or synthesizing separate components of the vehicle sound, then combining these components to produce a final sound. Using a physical model of the vehicle, the separate components of the vehicle sound are independently generated from vehicle control parameters characterizing the operating conditions of the vehicle. The components are then combined using mixers and equalizers to produce a realistic vehicle sound. The present technique allows independent control of the separate components of the vehicle sound, is not limited to specific vehicles, and does not require recorded sounds taking large amounts of storage space.

Music synthesizer system and method for simulating response of resonant digital waveguide struck by felt covered hammer

A musical sound synthesizer simulates interaction of a hammer having a compressible striking surface with a resonating medium. A digital waveguide resonator that simulates operation of a resonating medium and generates digital resonator waveforms representing signals propagating in said digital waveguide resonator. A hammer filter simulates the hammer striking the resonating medium and generates first and second hammer waveforms. The hammer filter includes a scattering junction that couples the hammer filter to the digital waveguide resonator. The hammer filter also includes a compression function that generates from the first and second hammer waveforms a compression value corresponding to compression of said simulated hammer, a stiffness function that generates a time varying stiffness coefficient as a function of the compression value, a excitation signal function that generates a hammer excitation signal as a function of hammer strike impulses, and a hammer function that generates the first hammer waveform as a function of the compression value, the hammer excitation signal and the second hammer waveform. The scattering junction transmits the digital resonator waveforms received from the digital waveguide resonator unchanged back into the digital waveguide resonator when the compression value corresponds to the hammer not being compressed and otherwise transmits a first time varying portion of the first digital resonator waveform combined with a second time varying portion of the digital resonator waveforms, wherein the first and second time varying portions of the first digital waveguide waveform and the digital resonator waveforms, respectively, are functions of the compression value.

The wave digital hammer: A computationally efficient traveling wave model of the piano hammer and the felt mallet

Recent work has led to traveling wave string and membrane models using the digital waveguide and the 2‐D digital waveguide mesh. This paper introduces a new development for these musical instrument models which extends their usefulness: a traveling wave model for the piano hammer, or felt mallet. When a mallet strikes an ideal membrane or string, it sinks down into it, feeling a pure resistive impedance. In the membrane case, the depression induces a circular traveling wave outward. If the membrane is bounded, reflected waves return to the strike point to throw the mallet away from the membrane. This complex mallet–membrane interaction can have very different and difficult to predict acoustical effects, particularly when a second or third strike occurs while the membrane is still in motion, as in a drum roll. The piano hammer, or felt mallet, is viewed as a nonlinear mass/spring (inductor/capacitor) system, the nonlinear spring representing the felt portion. By decomposing the system into appropriate trav...

In search of efficient physics‐based piano tone synthesis methods

The piano is a complicated, subtle tone‐producing device. Much work has been done toward understanding its physical and acoustical mechanisms. On the other hand, excellent results have been achieved in commercial sound synthesis, particularly through the sampling and processing of real piano sounds. The present work builds on digital waveguide string synthesis methods to develop physics‐based synthesis algorithms of piano and percussion sounds through appropriate physical models chosen with an eye toward psychoacoustics‐based simplifications and toward mathematical reformulation into efficient, physically calibratible digital filter structures. Recently developed physics‐based sound synthesis algorithms include: a shared‐loss string coupling structure modeling two‐stage decay, and a simplified string stiffness filter design, both calibratible from recorded sound data; a time‐varying wave digital piano hammer or mallet filter directly modeling nonlinear felt stiffness and hysteresis; membrane, plate, room,...

Applying Root-Locus Techniques to the Analysis of Coupled Modes in Piano Strings

Previous work in the study of coupled piano string behavior, e.g., by Weinreich and Nakamura, has focused analytically on the interaction of a pair of coupled modes, noting that the rest of the string modes couple similarly. The coupling of three or more modes, as occurs in sets of unison piano strings, is studied. Equivalent circuits (modeling a finite number of modes) of coupled piano strings can be written in state‐space form and their eigenvalues analyzed at various levels of detuning and coupling. Alternatively, the transfer functions of the system can often be written in a root‐locus analysis form, which lends a control‐theory perspective to the analysis. Often, an intuitive understanding of pole movement under variations in a single parameter, such as a single‐mode frequency or coupling coefficient, can be developed. Many effects, for example, two‐stage decay, can be understood in terms of system pole location. Three‐mode coupling is explored and interpreted, as is variation in coupling behavior at different string harmonics.

Equivalence of finite difference approximation and digital waveguide modeling for lossless, nondispersive media in one to three dimensions

The finite difference approximation method is commonly used to convert a differential equation into a recursive computation for computer simulation of an acoustic medium. Less well known is the digital waveguide modeling approach to the same problem, which is based on simulating the propagation of sampled traveling waves in the medium, and which implements losses and dispersion using digital filters applied to the traveling waves [Comput. Music. J., 74–91 (Winter 1992)]. It turns out the two methods are equivalent in rectilinear coordinates in one, two, and three dimensions, in the lossless, nondispersive case, provided the spatial sampling interval is chosen to be a specific constant (c in the one‐dimensional case) times the temporal sampling interval. Since the digital waveguide simulation technique requires far less computational effort, it can be used to both accelerate and increase the accuracy of numerical simulations of acoustic media.

A linear filter approximation to the hammer/string interaction for use in a commuted synthesis piano model

In commuted synthesis of string instruments, the soundboard/body resonator is commuted to the excitation point and replaced by its own impulse response [Smith and Van Duyne, elsewhere in this session]. Hence, the highly nonlinear hammer/string interaction must be replaced by a commutable linear filter. Using the wave digital hammer computational model of the piano hammer [ 3300(A) (1994)], it was observed that the force pulse of a hammer striking an infinite string was qualitatively similar to the impulse response of a second‐order filter with two real poles. Hence, good second‐ and higher‐order filter designs based on physical data were possible. However, multiple humps may appear in the hammer force pulse on a terminated string due to returning string waves. It was observed that the magnitude spectra of the single hump spectrum and the multiple hump spectrum were similar in bandwidth, differing only in a slight ringing in the lower spectrum due to the lowpassed combing effect of the returning string wav...

An efficient time‐domain model for the piano using commuted elements

A new time‐domain model for the piano is proposed which is extremely efficient for synthesizing piano sounds in hardware or software. The model includes multiple coupled strings, a nonlinear damped‐spring hammer model, and a linear soundboard and enclosure component which can have arbitrarily large order at very low cost. Simplifications based on the commutativity of linear, time‐invariant systems greatly reduce computational complexity [Comput. Music J. 74–91 (Winter 1992); Proc. International Computer Music Conference, Tokyo, pp. 56–71]. The hammer–string interaction is highly nonlinear and therefore does not commute with other components, in principle. However, by introducing a very mild approximation having little or no impact on the sound, commutativity can be achieved, leading to the enormous computational savings. This presentation will review the derivation of the piano synthesis model with special emphasis on the nonlinear hammer component. In its present form, a complete, two‐key piano can be synthesized in real time on a single Motorola DSP56001 signal processing chip with 8K words of static RAM and a clock rate of 25 MHz.