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Feinstrukturanalyse des Einschwingens eines Pianoklanges

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Autoregressive spectrum analysis (“AR”) is able to yield high resolution frequency spectra of very short segments of a signal record. Frequency resolution of these spectra is far better than in conventional Fourier analysis. Thus AR-spectrum analysis may lead to new insights, especially in the analysis of the fast varying, transient sounds of certain music instruments. Analysis of the initial portion of the piano sound reveals the fully developed set of partials in a first signal segment no longer than 2 fundamental periods. Another typical feature on the piano sound is spectral line splitting of higher partials - a phenomenon easily visible in the Fourier spectrum of long piano tone records. AR-spectrum analysis resolves this phenomenon into periodic frequency oscillations.


Die autoregressive Spektralanalyse (,,AR“) kann sehr detailreiche Spektren aus kurzen Signalausschnitten berechnen, wobei die aus der Fourieranalyse bekannten Grenzen des Frequenzauflösungsvermögens weit überschritten werden. Gerade bei der Analyse schnell veränderlicher, instationärer Klänge von Musikinstrumenten kann die AR-Methode zu neuen Erkenntnissen führen. Bei der Untersuchung des Einschwingens eines Pianotons stellte sich heraus, daß die gesamte, aus der Fourieranalyse viel längerer Aufnahmen bekannte Teiltonstruktur, schon nach den ersten beiden Grundwellenperioden voll entwickelt ist. Die spektrale Aufspaltung höherer Teiltöne im relativen Frequenzabstand von ca. 1% erscheint im AR-Bild als periodische Frequenzschwankung.


L'analyse fréquentielle autorégressive (AR) permet un calcul très détaillé du spectre d'un signal de très courte durée. Elle dépasse largement les limites de résolution de l'analyse classique par transformation de Fourier. Notamment elle fournit à l'analyse des sons non stationnaires et rapidement variables (transitoires des instruments de musique, par exemple) des informations nouvelles que la méthode de Fourier ne pouvait pas apporter. Ainsi l'analyse AR du transitoire d'attaque d'un son de piano a mis en évidence que les deux premières périodes du fondamental contiennent déjà l'ensemble des harmoniques du spectre obtenu par transformation de Fourier d'un enregistrement d'une durée beaucoup plus longue. Dans ce dernier, certains partiels d'ordre éléve paraissaient se décomposer en deux oscillations dont les fréquences différaient d'environ 1 %, alors que l'analyse AR montre qu'il s'agit plutôt d'une oscillation unique dont la fréquence subit des fluctuations périodiques.
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Document Type: Research Article

Publication date: April 1, 1989

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  • 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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