Geometrical interpretation of acoustic holography: Adaptation of the propagator and minimum quality guaranteed in the presence of errors

Martin, Vincent; Bourdon, Thibault Le; Arruda, José Roberto de França

doi:10.1016/j.jsv.2012.03.013

Cited by 1 publication

(2 citation statements)

References 11 publications

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“…The raw material of this section is to be found in Martin and Cariou (1997), in Le Bourdon (2009), and in Martin, Le Bourdon and Arruda (2012).…”

Section: Geometrical Interpretationmentioning

confidence: 99%

“…It is said "of reference" or "nominal" and written n p . The true pressure p is somewhere around this nominal value and is of the form As emphasized by Martin and Gronier (1998) and by Martin, Le Bourdon and Arruda (2012), this quantity may constitute a vicinity around the reference field containing all the perturbed fields such that their relative error is less than or equal to a given value of e . Ideally, a vicinity around n p should correspond to a vicinity around the efficiency…”

Section: Error Of the Objectivementioning

confidence: 99%

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The fundamental elements in certain inverse acoustic problems: their roles and interactions

Martin

2012

J. Braz. Soc. Mech. Sci. & Eng.

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Acoustic holography and holophony, wave field synthesis and active noise control are based on common elements which are causality, model, objective, and regularization. In the frequency domain (putting causality aside), a simple formulation states the influence-not the interaction-of errors of the model and objective and of regularization of the results. However, it does not give either an understanding or any relation of cause to effect. When the objective can be reached using the available model, regularization is not needed and the information liable to be extracted from this determined problem is poor, unlike in the overdetermined case when the model does not allow the objective to be reached. The geometrical interpretation of the over-determined problem written in the least-mean square sense could be a tool to enlighten the influences and interactions in question. After having shown the interest of the geometrical interpretation, a pseudo-analytical inverse problem in spherical holophony and a numerical problem in plane holography provide particular illustrations. From among the properties accessible, one is highlighted: in the case of a perfect objective but inaccurate model, its adaptation brings a decrease in the amount of regularization required and an improvement in the results.

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“…The raw material of this section is to be found in Martin and Cariou (1997), in Le Bourdon (2009), and in Martin, Le Bourdon and Arruda (2012).…”

Section: Geometrical Interpretationmentioning

confidence: 99%

Section: Error Of the Objectivementioning

confidence: 99%

The fundamental elements in certain inverse acoustic problems: their roles and interactions

Martin

2012

J. Braz. Soc. Mech. Sci. & Eng.

Self Cite

View full text Add to dashboard Cite

show abstract

Geometrical interpretation of acoustic holography: Adaptation of the propagator and minimum quality guaranteed in the presence of errors

Cited by 1 publication

References 11 publications

The fundamental elements in certain inverse acoustic problems: their roles and interactions

The fundamental elements in certain inverse acoustic problems: their roles and interactions

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