David P. Berners

A hybrid reverberation crossfading technique

Hybrid reverberators combine convolutional and feedback delay network (FDN) reverberators to exactly reproduce the psycoacoustically important reverberation impulse response onset while efficiently generating the needed late-field characteristics. A simple method for crossfading between the convolutional and FDN components of a hybrid reverberation is presented. It involves forming the convolutional impulse response as the windowed difference between the desired and FDN impulse responses. In this way, arbitrary windows may be applied to the convolution and FDN components of the hybrid reverberator impulse response in forming the cross-fade. For applications in which the impulse response onset depends on a parameter, a singular value decomposition is used to develop a low-rank approximation to the tabulated reverberation impulse response onsets. The approximation is the combination of a few fixed impulse responses, with parameter-dependent weights. An emulation of the EMT 140 plate reverberator is presented as a sample application.

On the use of Schrödinger’s equation in the analytic determination of horn reflectance

The flaring horn has traditionally been modeled in one dimension using piecewise conical or cylindrical elements. Acoustic properties within each element are known, and scattering between the elements is computed. Under the piecewise model, a shape for the wavefront of the acoustic disturbance within the horn is implicitly assumed (planar for cylindrical elements, spherical for conical elements). For horns of significant flare, the true wavefront shape will be neither planar nor spherical. A more general model is thus desirable. Here an alternate model is presented: The flaring horn is modeled according to Webster’s equation. A change of variables transforms the equation into the form of the Schrodinger wave equation using in one‐dimensional particle scattering. Boundary conditions can be derived directly from the physical dimensions of the horn, and the solution of the equation gives estimates of acoustic properties in terms of frequency dependent reflection and transmission coefficients. Here, Webster’s...

The discontinuous conical bore as a Sturm–Liouville problem

In some cases the reflection functions associated with the discontinuities in conical bores are growing exponentials [J. Martinez and J. Agul‐ lo, J. Acoust. Soc. Am. 84, 1613–1619 (1988)]. It is shown that discontinuities can be modeled by a Sturm–Liouville system using a pressurelike quantity as the dependent variable. For the subset of discontinuities exhibiting the growing exponential reflection function, the Sturm–Liouville potential function is an energy well. This well is shown to support exactly one trapped energy mode which corresponds to the growing exponential. It is shown that in the region surrounding the discontinuity for these systems, traveling Fourier components taken together with their reflected waves do not constitute a complete set and that the trapped mode is required to complete the set. On the other hand, for systems which do not exhibit the growing exponential, the Sturm–Liouville potential is an energy barrier with no trapped modes, and the Fourier components compose a complete set within the conical regions. Furthermore, a change of dependent variable can be used to go from a Sturm–Liouville description involving an energy well to one involving a barrier, thus eliminating the trapped mode.

Synthesis of brass tones using a driven lip model

Typical physical modeling synthesis methods for brass instruments contain a lip dynamics model and an acoustic flow model for the lips. Both elements contain nonlinearities, leading to a nonlinear feedback loop. Problems that arise with this type of system include difficulty in predicting the pitch of the synthesized tone and lack of robust methods for getting tones to ‘‘speak.’’ Elimination of the lip dynamics model leads to replacement of the nonlinear feedback system with a simpler nonlinear filtering system. In this model the lip reed is replaced by a zero impedance regulating valve which moves at the frequency of the desired output, according to measured lip data. Whereas for the conventional synthesis model, the frequency of synthesized sound is neither the resonant frequency of the lips nor the resonant frequency of the bore; in the case of the driven lip model, the synthesized frequency is exactly the same as the frequency at which the lip valve is driven. The driven model also guarantees that syn...

Horn reflectance update

The flared horn is modeled according to Webster’s equation. A change of variables transforms the equation into the form of the one‐dimensional Schrodinger wave equation. The Schrodinger form facilitates specification of arbitrary axisymmetric wavefronts for the acoustic disturbance within the horn. To provide a physically motivated choice of wavefront shape, Poisson’s equation is solved inside the horn subject to the boundary condition that the normal component of the potential gradient is zero at the boundary of the horn. Since the disturbance within the horn must satisfy the wave equation, the velocity potential satisfies Poisson’s equation when viscous effects and losses are ignored. Physical data from brass instrument bells are used to model musical horns using the Poisson solution, and results are compared to those obtained by traditional models which assume spherical wavefronts. Results are also compared to acoustic measurements.