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Equivalency of Lossless n-Tubes

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The inverse problem of the lossless speech production model does not have a unique solution, for a continuous set of tubes exists that have the same formant frequencies. This phenomenon is known in literature as articulatory compensation. In this paper we describe a method with which we can compute the continuous set of n-tubes that have the same formants. It follows that the problem can be handled analytically up to 10-tubes. We illustrate our analytic method on the basis of 4-tubes. It turns out that the values of the shape parameters of the tubes are restricted to certain intervals. Consequently, for some vowel sounds the corresponding 4-tube configurations must show particular shape characteristics, in spite of the articulatory compensation.

Zusammenfassung

Das inverse Problem des verlustfreien Modells der Sprachproduktion ist nicht eindeutig lösbar, weil eine unendliche Anzahl von Rohren mit denselben Formantfrequenzen existiert. Dieses Phänomen ist aus der Literatur als artikulatorische Kompensation bekannt. In dieser Arbeit beschreiben wir eine Methode, mit der die gesamte Anzahl von n-Rohren mit denselben Formantfrequenzen berechnet werden kann. Es zeigt sich, daß das Problem bis zu einer Zahl von 10 Rohren analytisch lösbar ist. Die analytische Methode wird an n Rohren demonstriert. Es zeigt sich, daß die Werte der Form-Parameter eines w-Rohres auf bestimmte Intervalle beschränkt sind. Daraus folgt, daß trotz der artikulatorischen Kompensation für einige Vokallaute die zugehörigen 4-Rohr-Kombinationen ähnliche Formcharakteristiken besitzen müssen.

Sommaire

Le problème inverse du modèle de la phonation par «-tubes sans pertes n'a pas de solution unique: il existe un ensemble continu de w-tubes qui possèdent les mêmes fréquences de formants. Ce phénomène est connu dans la littérature spécialisée sous le nom de «compensation articula-toire». Nous décrivons ici une méthode qui nous a permis de calculer l'ensemble des n-tubes qui possède les mêmes formants. Il en résulte que le problème inverse peut se traiter analytiquement jusqu'à la valeur 10 du nombre n de segments. Nous illustrons notre méthode sur l'exemple des 4-tubes. Il existe des restrictions pour les valeurs des paramètres décrivant la forme de la section du n-tube, ce qui entraîne la conséquence qu'en dépit de la compensation articulatoire les 4-tubes correspondant à certaines voyelles doivent posséder des formes particulières caractéristiques.
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Document Type: Research Article

Publication date: August 1, 1983

More about this publication?
  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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