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An Acoustic Signal Processing for Generalized Regression Analysis with Reduced Information Loss Based on Data Observed with an Amplitude Limitation

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As is well-known, the ordinary regression analysis method is confined to a simplified linear model of the estimation based on a Gaussian assumption and a least squares error criterion. However, it is often the case that actual phenomena cannot be exactly expressed by this simple model, owing to various complex factors. In this study, a regression analysis method reflecting various types of linear and/or nonlinear correlation properties among the variables is derived in a form appropriate when there exists an amplitude constraint on the observed data and the prediction of the response probability distribution. The effectiveness of the proposed method is confirmed experimentally by applying it to actual acoustical data.

Zusammenfassung

Bekanntlich ist die iibliche Regressionsanalyse auf ein vereinfachtes Schätzmodell beschränkt, das auf der Gauss'schen Annahme und dem Kriterium der kleinsten Fehlerquadrate beruht. Allerdings können tatsächliche Beobachtungen wegen ihrer Komplexität mit diesem einfachen Modell oft nicht genau beschrieben werden. In dieser Untersuchung wird eine Methode der Regressionsanalyse abgeleitet, die verschiedene Typen von linearen und/oder nichtlinearen Korrelationseigenschaften zwischen den Variablen berücksichtigt, wobei einer Amplitudenbegrenzung der beobachteten Daten und der Vorhersage der Wahrscheinlichkeitsverteilung der Ausgangsgröße Rechnung getragen wird. Die Wirksamkeit der vorgeschlagenen Methode wird experimentell durch Anwendung auf tatsächliche akustische Daten bestätigt.

Sommaire

Il est bien connu que l'analyse de régression ordinaire est limitée à un modèle linéaire simplifié basé sur l'hypothése d'une distribution gaussienne et un critère d'erreur de moindres carrés. Cependant, il arrive fréquemment que des phénomènes réels ne puissent pas être representés par ce modèle simplifié, è cause de divers facteurs complexes. Dans cette étude, nous introduisons une méthode d'analyse de régression qui rend compte de différents types de corrélations linéaires ou non entre les variables, et sous une forme appropriée pour le cas où il y a des contraintes d'amplitude sur les données observées et pour une détermination précise de la densité de probabilité de reponse. On teste l'efficacité de la méthode sur des données acoustiques réelles.
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Document Type: Research Article

Publication date: March 1, 1995

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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