Roberto A. Tenenbaum

An exact solution for the one‐dimensional elastic wave equation in layered media

A new approach to the direct scattering problem in one‐dimensional inhomogeneous bodies is presented. A general formulation considering density, wave speed, and cross section variation is introduced and a compact form for the wave equation in the characteristic plane, with a generalized acoustical impedance profile as a parameter, is established with the aid of a nonsingular variable transformation. The wave propagation pattern in layered (or discretized continuous) media is then examined and an exact algebraic solution for the reflected wave is obtained. The resulting formula is adequate to an arbitrary input pulse, furnishing a quick computation of all multiple reflection contributions to the final echo.

Hybrid method for numerical simulation of room acoustics with auralization: part 1 - theoretical and numerical aspects

A new hybrid simulation method for room acoustics is presented. It is grounded on two well known numerical simulation techniques for room acoustics. The hybrid method takes geometric acoustics for granted and uses an improved version of the classical ray-tracing technique for computing the specular reflections and a slightly modified energy transition method for simulating the diffuse reflections. The impulse responses (IRs) are then computed by superposition of the specular and diffuse ones. The reverberant part of the IRs gains a much more realistic aspect than the one obtained from either ones method alone. Both the ray-tracing technique and the energy transition method are reviewed and some improved features are discussed. The sound source and the receiver modeling are presented, including a new method for simulating the head related transfer functions (HRTFs), and based on the wavelet technique, which provides a shorter time computation of the binaural impulse responses for auralization purposes. In a companion paper, entitled Hybrid method for numerical simulation of room acoustics: Part 2 - Validation of the computational code RAIOS 3, a validation of the method in an international inter-comparison with other softwares and measurements data is presented, showing the efficiency and the accuracy of the proposed hybrid method over non-hybrid ones.

Low-order modeling of head-related transfer functions using wavelet transforms

In this paper, an efficient method for modeling head-related transfer functions (HRTFs) of an auralization system is presented. The proposed model is based on the decomposition of the impulse response of the HRTFs by wavelet transforms. Through an analysis of the HRTF energy content per subband it is shown how the model can be reduced without introducing considerable error in the magnitude and phase frequency responses. As a result of the proposed technique, the low-order model has approximately 30% of the number of coefficients of the original HRTF, which represents an important reduction in the computational cost of an auralization system implementation.

A fast algorithm to solve the inverse scattering problem in layered media with arbitrary input

A new sequential algorithm to solve the one‐dimensional inverse scattering problem in layered media with arbitrary inlet pulse is presented. The procedure consists of the mathematical inversion of the exact algebraic solution for the direct problem derived in Tenenbaum and Zindeluk [J. Acoust. Soc. Am. XX, XXXX–XXXX (1992)] and features computational efficiency together with improved numerical stability. Simulated examples of successful impedance profile identification with noisy data are reported and a detailed analysis of the stability improvement is provided. Impact tests on variable cross‐section long bars monitored with strain gauges are also reported and the method is applied to actual parameter profile identification, with success.

A NEW TECHNIQUE TO IDENTIFY ARBITRARILY SHAPED NOISE SOURCES

Acoustic intensity is one of the available tools for evaluating sound radiation from vibrating bodies. Active intensity may, in some situations, not give a faithful insight about how much energy is in fact carried into the far field. It was then proposed a new parameter, the supersonic acoustic intensity, which takes into account only the intensity generated by components having a smaller wavenumber than the acoustic one. However, the method is only efective for simple sources, such as plane plates, cylinders and spheres. This work presents a new technique, based on the Boundary Elements Method and the Singular Value Decomposition, to compute the supersonic acoustic intensity for arbitrarily shaped sources. The technique is based in the Kirchoff-Helmholtz equation in a discretized approach, leading to a radiation operator that relates the normal velocity on the sources surface mesh with the pressure at grid points located in the field. Then, the singular value decomposition technique is set to the radiation operator and a cutoff criterion is applied to remove non propagating components. Some numerical examples are presented.

Damage Identification in Bars with a Wave Propagation Approach: Performance Comparison of Five Hybrid Optimization Methods

The formulation and solution of the inverse problem of damage identification based on an one-dimensional wave propagation approach are presented in this paper. Time history responses, obtained from pulse-echo synthetic experiments, are used to damage identification. The identification process is built on the minimization of the squared residue between the synthetic experimental echo, obtained by using a sequential algebraic algorithm, and the corresponding analytical one. Fivedifferent hybrid optimization methods areinvestigated. The hybridization is performed combining the deterministic Levenberg-Marquardt method and each one of the following stochastic techniques: The Particle Swarm Optimization; the Luus-Jaakola optimization method; the Simulated Annealing method; the Particle Collision method; and a Genetic Algorithm. A performance comparison of the five hybrid techniques is presented. Different damage scenarios are considered and, in order to account for noise corrupted data, signals with 10 dB of signal to noise ratio are also considered. It is shown that the damage identification procedure built on the Sequential Algebraic Algorithm yielded to very fast and successful solutions. In the performance comparison, it is also shown that the hybrid technique combining the Luus-Jaakola and the Levenberg-Marquardt optimization methods provides the faster damage recovery.

Roof Configurations, Room Quality Parameters and Musical Performances: An Analysis of the São Paulo Hall

The São Paulo Hall (SPH) is recognized by musicians and musical critics in general by its good acoustical quality. Having geometric dimensions similar to the ones of some famous concert halls, it has as an important feature a variable acoustics due to its movable roof, which is employed by musicians to tune the room according to the musical style, in an ad hoc procedure. This work addresses the acoustical quality of the São Paulo Hall and the dependence of its acoustics on the roof configuration. Impulse responses for one source, eight microphone and two dummy head positions, using the sweep-sine technique with pre-emphasis, were obtained for seven distinct roof configurations. Several details of the measurement procedures to ensure good accuracy and repetitiveness are widely discussed. The measurement results were then used to compute the main room acoustical quality parameters, for each octave band between 63 Hz and 8 kHz. The spatial average and deviation of these data are presented as a function of the frequency band. The influence of the roof configurations on the obtained acoustical parameters is then presented and discussed. Furthermore, comparative plots among some acoustical parameters presented by São Paulo Hall at the chosen roof configurations and two famous and representative halls from the classical and romantic periods are reported. It is concluded that the movable roof is very effective in modifying the room acoustics and that the musicians ad hoc choices seems to be quite good.

Acoustical analysis of a variable roof configuration concert hall: The São Paulo Hall

The Sao Paulo Hall (SPH) is recognized by musicians and musical critics in general by its good acoustical quality. It has, as an important feature, variable acoustics due to its movable roof, which is employed by musicians to tune the room according to the musical style. This work addresses the acoustical quality of SPH and its dependence on the roof configuration. Impulse responses for one source, eight microphone and two dummy head positions, using the sweep‐sine technique with pre‐emphasis, were obtained for seven roof configurations. Some details of the measurement procedure to ensure good accuracy are discussed. The measurement results were then used to compute the main room acoustical quality parameters, for each octave band between 63 and 8000 Hz. The spatial average and deviation of these data are presented as a function of the frequency band. The influence of the roof configurations on the obtained acoustical parameters is also discussed. Furthermore, comparative plots among SSP at the chosen roof configurations and two famous and representative halls from the classical and romantic periods are reported and discussed. It is concluded that the movable roof is very effective in modifying the room acoustics and that the musicians choices are quite good.

Low-order modeling and grouping of HRTFs for auralization using wavelet transforms

An efficient method for modeling head-related transfer functions (HRTFs) of an auralization system is presented. The proposed model is based on the decomposition of the impulse response of the HRTFs by wavelet transforms and on the grouping of such functions for close directions. Through an analysis of the HRTF energy content per subband, it is shown how the model can be reduced without introducing considerable errors in the magnitude and phase frequency responses. As a result of the proposed technique, a significant reduction in the processing time of the auralization process is obtained by a low-order model which has approximately 30% of the number of coefficients of the original HRTF and by a reduction in the number of HRTF directions to less than 10%.

Nonsmooth impedance profile identification using reflection data

Many works published about identification of acoustic properties of inhomogeneous media present methods based on the assumption that these properties vary smoothly along the propagation direction. This work presents a comparison between two time‐domain sequential inverse methods for evaluation of either smooth or nonsmooth impedance profiles of transversely infinite media excited by plane waves at normal incidence. Sequential methods, also known as layer stripping methods, despite having the disadvantage of being quite sensitive to noise in the measured signal, are faster than other approaches, such as those that use global optimization techniques. The first method in the comparison [R. A. Tenenbaum and M. Zindeluk, J. Acoust. Soc. Am. 92, 3364–3369 (1992)] assumes a smooth profile by using a transformation of variables, which neglects the refraction effects between two consecutive layers. The second one, more general, performs some more calculations since it takes these effects into account, paying the p...