Implementation of the Radiation Characteristics of Musical Instruments in Wave Field Synthesis Applications

In this thesis a method to implement the radiation characteristics of musical instruments in wave field synthesis systems is developed. It is applied and tested in two loudspeaker systems.Because the loudspeaker systems have a comparably low number of loudspeakers the wave field is synthesized at discrete listening positions by solving a linear equation system. Thus, for every constellation of listening and source position all loudspeakers can be used for the synthesis. The calculations are done in spectral domain, denying sound propagation velocity at first. This approach causes artefacts in the loudspeaker signals and synthesis errors in the listening area which are compensated by means of psychoacoustic methods. With these methods the aliasing frequency is determined by the extent of the listening area whereas in other wave field synthesis systems it is determined by the distance of adjacent loudspeakers. Musical instruments are simplified as complex point sources to gain, store and propagate their radiation characteristics. This method is the basis of the newly developed “Radiation Method” which improves the matrix conditioning of the equation system and the precision of the wave field synthesis by implementing the radiation characteristics of the driven loudspeakers. In this work, the “Minimum Energy Method” — originally developed for acoustic holography — is applied for matters of wave field synthesis for the first time. It guarantees a robust solution and creates softer loudspeaker driving signals than the Radiation Method but yields a worse approximation of the wave field beyond the discrete listening positions. Psychoacoustic considerations allow for a successfull wave field synthesis: Integration times of the auditory system determine the spatial dimensions in which the wave field synthesis approach works despite different arrival times and directions of wave fronts. By separating the spectrum into frequency bands of the critical band width, masking effects are utilized to reduce the amount of calculations with hardly audible consequances. By applying the “Precedence Fade”, the precedence effect is used to manipulate the perceived source position and improve the reproduction of initial transients of notes. Based on Auditory Scene Analysis principles, “Fading Based Panning” creates precise phantom source positions between the actual loudspeaker positions. Physical measurements, simulations and listening tests prove evidence for the introduced methods and reveal their precision. Furthermore, results of the listening tests show that the perceived spaciousness of instrumental sound not necessarily goes along with distinctness of localization. The introduced methods are compatible to conventional multi channel audio systems as well as other wave field synthesis applications.In dieser Arbeit wird eine Methode entwickelt, um die Abstrahlcharakteristik von Musikinstrumenten in Wellenfeldsynthesesystemen zu implementieren. Diese wird in zwei Lautsprechersystemen umgesetzt und getestet. Aufgrund der vergleichsweise geringen Anzahl an Lautsprechern wird das Schallfeld an diskreten Hörpositionen durch Lösung eines linearen Gleichungssystems resynthetisiert. Dadurch können für jede Konstellation aus Quellen- und Hörposition alle Lautsprecher für die Synthese verwendet werden. Hierzu wird zunächst in Frequenzebene, unter Vernachlässigung der Ausbreitungsgeschwindigkeit des Schalls gerechnet. Dieses Vorgehen sorgt für Artefakte im Schallsignal und Synthesefehler im Hörbereich, die durch psychoakustische Methoden kompensiert werden. Im Vergleich zu anderen Wellenfeldsyntheseverfahren wird bei diesem Vorgehen die Aliasingfrequenz durch die Größe des Hörbereichs und nicht durch den Lautsprecherabstand bestimmt. Musikinstrumente werden als komplexe Punktquellen vereinfacht, wodurch die Abstrahlung erfasst, gespeichert und in den Raum propagiert werden kann. Dieses Vorgehen ist auch die Basis der neu entwickelten “Radiation Method”, die durch Einbeziehung der Abstrahlcharakteristik der verwendeten Lautsprecher die Genauigkeit der Wellenfeldsynthese erhöht und die Konditionierung der Propagierungsmatrix des zu lösenden Gleichungssystems verbessert. In dieser Arbeit wird erstmals die für die akustische Holografie entwickelte “Minimum Energy Method” auf Wellenfeldsynthese angewandt. Sie garantiert eine robuste Lösung und erzeugt leisere Lautsprechersignale und somit mehr konstruktive Interferenz, approximiert das Schallfeld jenseits der diskreten Hörpositionen jedoch schlechter als die Radiation Method. Zahlreiche psychoakustische Überlegungen machen die Umsetzung der Wellenfeldsynthese möglich: Integrationszeiten des Gehörs bestimmen die räumlichen Dimensionen in der die Wellenfeldsynthesemethode — trotz der aus verschiedenen Richtungen und zu unterschiedlichen Zeitpunkten ankommenden Wellenfronten — funktioniert. Durch Teilung des Schallsignals in Frequenzbänder der kritischen Bandbreite wird unter Ausnutzung von Maskierungseffekten die Anzahl an nötigen Rechnungen mit kaum hörbaren Konsequenzen reduziert. Mit dem “Precedence Fade” wird der Präzedenzeffekt genutzt, um die wahrgenommene Schallquellenposition zu beeinflussen. Zudem wird dadurch die Reproduktion transienter Einschwingvorgänge verbessert. Auf Grundlage von Auditory Scene Analysis wird “Fading Based Panning” eingeführt, um darüber hinaus eine präzise Schallquellenlokalisation jenseits der Lautsprecherpositionen zu erzielen. Physikalische Messungen, Simulationen und Hörtests weisen nach, dass die neu eingeführten Methoden funktionieren und zeigen ihre Präzision auf. Auch zeigt sich, dass die wahrgenommene Räumlichkeit eines Instrumentenklangs nicht der Lokalisationssicherheit entspricht. Die eingeführten Methoden sind kompatibel mit konventionellen Mehrkanal-Audiosystemen sowie mit anderen Wellenfeldsynthesesystemen

Analysis of an existing experiment on the interaction of acoustic waves with a laminar boundary layer

The hot-wire anemometer amplitude data contained in the 1977 report of P. J. Shapiro entitled, ""The Influence of Sound Upon Laminar Boundary'' were reevaluated. Because the low-Reynolds number boundary layer disturbance data were misinterpreted, an effort was made to improve the corresponding disturbance growth rate curves. The data are modeled as the sum of upstream and downstream propagating acoustic waves and a wave representing the Tollmien-Schlichting (TS) wave. The amplitude and phase velocity of the latter wave were then adjusted so that the total signal reasonably matched the amplitude and phase angle hot-wire data along the plate laminar boundary layer. The revised rates show growth occurring further upstream than Shapiro found. It appears that the premature growth is due to the adverse pressure gradient created by the shape of the plate. Basic elements of sound propagation in ducts and the experimental and theoretical acoustic-stability literature are reviewed

The plenacoustic function and its applications

This thesis is a study of the spatial evolution of the sound field. We first present an analysis of the sound field along different geometries. In the case of the sound field studied along a line in a room, we describe a two-dimensional function characterizing the sound field along space and time. Calculating the Fourier transform of this function leads to a spectrum having a butterfly shape. The spectrum is shown to be almost bandlimited along the spatial frequency dimension, which allows the interpolation of the sound field at any position along the line when a sufficient number of microphones is present. Using this Fourier representation of the sound field, we develop a spatial sampling theorem trading off quality of reconstruction with spatial sampling frequency. The study is generalized for planes of microphones and microphones located in three dimensions. The presented theory is compared to simulations and real measurements of room impulse responses. We describe a similar theory for circular arrays of microphones or loudspeakers. Application of this theory is presented for the study of the angular sampling of head-related transfer functions (HRTFs). As a result, we show that to reconstruct HRTFs at any possible angle in the horizontal plane, an angular spacing of 5 degrees is necessary for HRTFs sampled at 44.1 kHz. Because recording that many HRTFs is not easy, we develop interpolation techniques to achieve acceptable results for databases containing two or four times fewer HRTFs. The technique is based on the decomposition of the HRTFs in their carrier and complex envelopes. With the Fourier representation of the sound field, it is then shown how one can correctly obtain all room impulse responses measured along a trajectory when using a moving loudspeaker or microphone. The presented method permits the reconstruction of the room impulse responses at any position along the trajectory, provided that the speed satisfies a given relation. The maximal speed is shown to be dependent on the maximal frequency emitted and the radius of the circle. This method takes into account the Doppler effect present when one element is moving in the scenario. It is then shown that the measurement of HRTFs in the horizontal plane can be achieved in less than one second. In the last part, we model spatio-temporal channel impulse responses between a fixed source and a moving receiver. The trajectory followed by the moving element is modeled as a continuous autoregressive process. The presented model is simple and versatile. It allows the generation of random trajectories with a controlled smoothness. Application of this study can be found in the modeling of acoustic channels for acoustic echo cancellation or of time-varying multipath electromagnetic channels used in mobile wireless communications