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Journal of the Acoustical Society of America

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Sep 1970

Volume 48, Issue 3A, pp. 603-628


Laser Heterodyne System for Measurement and Analysis of Vibration

F. J. Eberhardt and F. A. Andrews

J. Acoust. Soc. Am. Volume 48, Issue 3A, pp. 603-609 (1970); (7 pages) | Cited 4 times

Online Publication Date: 03 Aug 2005

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The calibration and use of a laser heterodyne system for nonsinusoidal vibration measurements are described. A frequency‐shifted beam is heterodyned in a photomultiplier with an unshifted central light beam that has been phase modulated by motion of a reflecting surface. The output of the phototube is passed through a limiter‐discriminator receiver, and then through an integrator resulting in a linear reproduction of the surface vibration as long as the frequency‐amplitude product is within limits. The linearity and calibration technique has been tested out to a product of 13 kHz × 4700 Å. A minimum amplitude measurement of 3.5 Å was obtained. Measurement of time delay or spatial cross‐correlation functions is demonstrated, using two heterodyne detectors.

Spatial Detectability Characteristics of One‐, Two‐, and Three Dimensional Array Receiving Systems

Robert W. Cline and William D. Gregg

J. Acoust. Soc. Am. Volume 48, Issue 3A, pp. 610-621 (1970); (12 pages)

Online Publication Date: 03 Aug 2005

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The signal detectability gain performance index, for array receiving systems, is employed to derive the spatial detectability characteristics of some simple one‐, two‐, and three‐dimensional configurations. Analytical results are obtained in terms of array geometry, dimensionality, and space‐time correlation structure of the interference field. The analytical treatment is predicated upon decision theoretic foundations for waveform signal and noise structures. Homogeneous and isotropic Gaussian interference fields are assumed. Particular array‐geometry examples treated are linear, triangular, rectangular, and isosceles pyramidal, employing three and four elements. Analyses of the spatial detectability gain characteristics are achieved for the above configurations. Illustrations of the detectability gain are given in a plane passed through the array coordinate system, for 360° about the main lobe, with various permutations in array parameters. Various advantages of the two‐ and three‐dimensional configurations, over the one‐dimensional configuration and the associated conditions, are discussed.

Distribution of the Sum of Clipped Waveforms in Terms of the Multivariate Input‐Amplitude Distribution

Edward S. Eby

J. Acoust. Soc. Am. Volume 48, Issue 3A, pp. 622-627 (1970); (6 pages)

Online Publication Date: 03 Aug 2005

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For an arbitrary multivariate input‐amplitude distribution, it is shown that the density of the sum of clipped versions of the input waveforms is linearly related to the sums of the clipped moments of each order. This linear dependence implies that the vector of clipped‐moment sums must lie within an N‐dimensional tetrahedral restriction region in a moment space and provides a necessary condition on the multivariate input distribution. Previous derivations of the density and moments of the sum of clipped waveforms were restricted to the case in which the components of the input vector were statistically independent.
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Probability Density Function of Time‐Average Power and Log (Power)

P. P. Nuspl

J. Acoust. Soc. Am. Volume 48, Issue 3A, pp. 628-628 (1970); (1 page)

Online Publication Date: 03 Aug 2005

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