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Jun 1979

Volume 65, Issue S1, pp. S2-S142

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back to top Session W. Underwater Acoustics IV; Signal Processing
Contributed Papers
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Cross‐sensor beamforming for a U‐shaped array (A)

Homer P. Bucker

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S61-S61 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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A U‐shaped array can be made using two surface floats, an underwater anchor, the line of sensors, and a horizontal fish line to maintain array configuration. Conventional beam forming of this array will result in side‐lobe problems. It will be shown how cross‐sensor beamforming can be used to detect weak acoustic targets that have lower levels than the side lobes of stronger targets.
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Comparison of shifted sideband and conventional beamforming techniques (A)

R. A. Mucci and R. G. Pridham

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S61-S61 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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For many array configurations the exact time delays required for beamsteering impose prohibitingly large sample rate requirements on digital beamformer implementation. This necessitates the use of approximate time delays to achieve moderate sample rate requirements. For conventional beamformer implementations this degrades the sidelobe structure of the beampatterns. This degradation is also experienced by shifted sideband beamformers (SSB) which utilize frequency translated single sideband representations of the input signals [J. Acoust. Soc. Am. 64, S116(A) (1978)]. However, since beamsteering is performed on translated signals rather than on the original signals, degradation of the beampattern for the SSB is less sensitive to absolute time‐delay errors than for the conventional approach. This result is supported analytically and by examples. The phase shift beamformer, a limiting case of both a frequency domain beamformer and the SSB, is considered. Beamsteering errors experienced by the phase shift beamformer at frequencies other than that for which it was designed are discussed. Analytical results and examples are presented which demonstrate that these errors can be eliminated with the SSB.
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Approximations to Dolph‐Cbebyshev data windows (A)

John C. Burgess

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S61-S61 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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A family of optimum data windows was presented recently [J. C. Burgess, J. Acoust. Soc. Am. 62, S51(A) (1977)]. These windows are optimum in the sense that their spectral representations have the narrowest main lobes possible for a specified ratio of maximum side lobe amplitude to main lobe amplitude subject to the condition that the windows are described by Fourier series having very few nonzero coefficients. The process by which the Fourier coefficients are determined is equivalent to fixing the amplitude of one lobe in the spectral representation for each nonzero coefficient. A Fourier series having M + 1 coefficients thus controls the amplitudes of M side lobes. The Dolph‐Chebyshev windows have the narrowest main lobes possible, and all side lobes for each window have the same level. The windows described by Burgess can thus be thought of as approximations to Dolph‐Chebyshev windows. For M + 1 = 4 (i.e., four nonzero Fourier coefficients), the approximations have main lobe widths less than 5% wider than the corresponding Dolph‐Chebyshev windows.
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Individual module directivity pattern calculation for elements of a close‐packed array (A)

Stephen C. Thompson

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S61-S61 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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The radiation pattern of a single transducer can be calculated in many cases of interest. However when several such transducers are arranged in a close‐packed array, mutual impedance effects modify the individual element directivities. The effects are pronounced near the element resonance frequency, where such arrays are commonly operated. It has been standard practice to use measured individual element patterns when accurate beam pattern calculations and optimizations are undertaken. Thus the array must be built before its optimal performance can be predicted, making geometrical changes to the design difficult and expensive. This paper presents a method of including the mutual impedances in the individual element directivity calculation. For an array of N elements the method produces a set of 2N linear equations for the real and imaginary parts of the response of each element when the excitation frequency and plane wave arrival angle are given. The method requires knowledge of the acoustic mutual impedances between all pairs of elements, the acoustic self‐impedances, the mechanical impedance of each of the individual element radiating areas, and the directivity pattern of each element in the absence of all mutual effects.
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Effect of element failure and random errors in amplitude and phase on the sidelobe level attainable with a linear array (A)

Dan J. Ramsdale and Roger A. Howerton

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S61-S62 (1979); (2 pages)

Online Publication Date: 11 Aug 2005

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Low sidelobe levels may be a crucial factor in the success of achieving high gain using linear receiving arrays, since the level of the sidelobes determines the degree to which noisy nearby sources can be prohibited from interfering with the detection of a weak source on a different azimuth. In real world experiments at sea, one frequently operates with an array which has not only errors in amplitude and phase between channels but also dead elements. The effect of random errors in both amplitude and phase is to yield a sidelobe level of the average beam pattern which is the sum of the error‐free pattern and an additional level due to the random errors. The sidelobe level due to the random errors depends upon the details of the amplitude shading function, the distribution function from which the random errors are drawn, and increases with the mean square value of the errors. Thus, given rms values of amplitude and phase errors, there is a practical limit to which the sidelobes can be reduced by amplitude shading the array. The effect of element failure on the sidelobe level can be drastic and depends on the sum of the amplitude weights of the dead elements. Thus, a failure of a highly‐weighted element will have a greater effect on the sidelobe level than the failure of two or three whose combined weights are less. [Work supported by NAVMAT.]
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Simultaneous estimation of target range and bearing (A)

D. P. Skinner

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S62-S62 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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Simultaneous estimation of the range and bearing of a point target from a moving platform is discussed. The proposed approach exploits the relation between Doppler and bearing by transmitting into a broad sector and separating targets in bearing on the basis of their Doppler. The design of large time bandwidth product signals for this purpose is examined and a comparison is made of the range‐bearing ambiguity function for simple waveform types. This work concludes with a brief inspection of the effects of focusing error on the range‐bearing ambiguity function.
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Directivity index of partially random sonobuoy arrays (A)

J. V. Thorn, N. O. Booth, and J. C. Lockwood

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S62-S62 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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The directivity index DI of the partially random sonobuoy array described in a previous paper [J. Acoust. Soc. Am. 64, S123(A) (1978)] is analyzed. The analysis is based on the definition of DI as the ratio in decibels of the power received by a single omnidirectional hydrophone of unity gain to the array power normalized to unity maximum gain. The array power is a random variable. Its expected value is used in the definition of DI to define the “nominal DI.” The variance of the array power provides a measure of the variability of the DI among the members of an ensemble. The type of partially random array analyzed consists of N elements arranged in vertical strings of M elements each. With N constant, the variance of the array power tends to increase as M is increased. The increase is the result of the increasingly large contribution to the array power of the side‐lobes at the main lobe elevation, which have a relatively large variance. The effects of the number of elements per string on the nominal DI and on the variability of the DI are examined quantitatively.
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The role of fading statistics in channel matching (A)

Edgar H. Neal

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S62-S62 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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It is well known that sonar system performance varies considerably when fixed amount of source energy is divided among N diversity signals when the fading is Rayleigh. This paper reviews the Rayleigh results and establishes similar results for chi‐square, Rice, and log‐normal fading. Performance curves are included for both search and communication systems.
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A generalized frequency processor (A)

J. W. Young

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S62-S62 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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The signal received by a Doppler navigation sonar (or radar) has the character of narrow bandwidth noise [F. B. Berger, IRE Trans. Aero. Nay. Elec. ANE‐4, 103 (1957)]. The desired information is some characteristic of the spectrum of this process such as the center of power or a higher order moment. A variety of hardware implementations of frequency measurements systems have been used for this purpose, but their relationship to spectral analysis has remained somewhat obscure. In this paper, it is shown using the analytic signal concept that a “frequency discriminator” computes the first moment of the power spectrum. The approach is generalized to develop a signal processing architecture which can compute an arbitrary function of the power spectrum.
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Multipath induced corruption of bearing estimation by split ring hydrophones (A)

Jack E. Cater

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S62-S62 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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A single acoustic plane wave, insonifying a four piece, split ring hydrophone, produces voltages in orthogonal directions proportional to the cosine and sine of the bearing to the source with respect to some reference direction. In certain circumstances, e.g., shallow water, multipath conditions exist where comparable energy contributions are made from several paths along the same bearing. If the contributions are in phase or nearly in phase at the hydrophone, voltages similar to those of the single plane wave case are observed. In general, however, the phases are different and the voltages consist of series of products of Bessel functions related to phase difference, hydrophone radius and frequency, and sines and cosines of the fundamental frequency and harmonics of the source.
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Acoustic imaging by spatial correlation (A)

Darrell R. Jackson and Kou‐Ying Moravan

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S62-S62 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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Analysis and computer simulation based on the point scatterer model have been used to show that high‐resolution images can be produced by forming the temporal cross‐correlation of the echo signals received by two or more transducers, with angular resolution on the order of the pulse resolution divided by the receiver spacing. With two receivers, the correlator output constitutes a one‐dimensional image, with correlation magnitude corresponding to “brightness” and correlator shift proportional to azimuth. The image contains a noisy background having a level approximately equal to (T/T0)1/2, where T is the pulse resolution, T0 is the duration of the echo from the object to be imaged, and unity is the maximum possible correlator output. The desired image is a convolution of the signal autocorrelation with the angular density function for the acoustic highlights of the object. This convolution results in a smearing of the image, which is reduced if relative bandwidths on the order of one decade are used. Possible applications of this technique are underwater imaging for divers and ultrasonic medical diagnosis. [Funded by Naval Sea Systems Command under Contract N00024‐78‐C‐6018.]
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