George E. Ioup

Properties of higher‐order correlations and spectra for bandlimited, deterministic transients

Higher‐order correlations and spectra may be used for detection, time delay estimation, classification, and discrimination of signals. For these applications, a detailed knowledge of their attributes can be highly useful. In this paper, the properties of the bicorrelation and tricorrelation of bandlimited deterministic transients, i.e., energy signals, and their spectra, the bispectrum and trispectrum are studied. Bandlimited transients that contain frequencies down to and including zero and those that have a nonzero lower cutoff frequency are both considered. Using symmetries inherent in the bispectrum of a signal, the entire bispectrum can be mapped from bispectral elements defined in two polygons, one for the unaliased and one for the aliased domain, each of which is one‐twelfth the area of its total domain. The nonredundant unaliased region of the trispectrum is contained in two principal unaliased polyhedra, each replicated 48 times to reproduce the full trispectrum. If there is aliasing in the trisp...

Convergence of the van Cittert iterative method of deconvolution

Conditions necessary for the convergence of the van Cittert iterative method of deconvolution are studied. Conditions that can be expressed in the function domain are derived, some of which are readily apparent restrictions on the shape of the impulse response. The position of the response function along the abscissa is considered, since the shifting of the function can influence convergence. Only real, piecewise-analytic responses with pointwise Fourier transforms and pointwise Fourier inversion are considered.

Assessing the Deepwater Horizon oil spill impact on marine mammal population through acoustics: Endangered sperm whales

Long-term monitoring of endangered species abundance based on acoustic recordings has not yet been pursued. This paper reports the first attempt to use multi-year passive acoustic data to study the impact of the Deepwater Horizon oil spill on the population of endangered sperm whales. Prior to the spill the Littoral Acoustic Demonstration Center (LADC) collected acoustic recordings near the spill site in 2007. These baseline data now provide a unique opportunity to better understand how the oil spill affected marine mammals in the Gulf of Mexico. In September 2010, LADC redeployed recording buoys at previously used locations 9, 25, and 50 miles away from the incident site. A statistical methodology that provides point and interval estimates of the abundance of the sperm whale population at the two nearest sites is presented. A comparison of the 2007 and the 2010 recordings shows a decrease in acoustic activity and abundance of sperm whales at the 9-mile site by a factor of 2, whereas acoustic activity and abundance at the 25-mile site has clearly increased. This indicates that some sperm whales may have relocated farther away from the spill. Follow-up experiments will be important for understanding long-term impact.

Detection of Oscillatory and Impulsive Transients Using Higher Order Correlations and Spectra

Higher‐order cross and ordinary correlation detectors are applied to four deterministic transients contaminated by uncorrelated Gaussian noise only. Histograms and moments are used to examine the properties of the signals and their effect on detector performance. Receiver operating characteristic (ROC) curve analysis and limiting signal‐to‐noise ratios for ‘‘good’’ detection provide comparative measures for different detectors. Probability density functions of detection ordinate values of signal‐present and noise‐only correlations are used to explain ROC curve behavior. Using a known source, the cross‐correlation detector performs better than the higher‐order correlation detectors for each transient studied. However, for an unknown narrow pulse source signal, the bicorrelation and tricorrelation detectors outperform the cross‐correlation detector. In contrast, the bicorrelation detector performs very poorly for low‐frequency narrow‐band signals with a small third moment embedded in uncorrelated Gaussian n...

Approximating the finite square well with an infinite well: Energies and eigenfunctions

Polynomial expansions are used to approximate the equations of the eigenvalues of the Schrodinger equation for a finite square potential well. The technique results in discrete, approximate eigenvalues which, it is shown, are identical to the corresponding eigenvalues of a wider, infinite well. The width of this infinite well is easy to calculate; indeed, the increase in width over that of the finite well is simply the original width divided by the well strength. The eigenfunctions of this wider, infinite well, which to first order has the same width for the ground state and all excited states, are also good approximations to the exact eigenfunctions of the finite well. These approximate eigenfunctions and eigenvalues are compared to accurate numeric calculations and to other approximations from the literature.

Variability in higher order statistics of measured shallow-water shipping noise

Many underwater acoustic signal processing algorithms are designed for use in stationary and/or Gaussian noise. While these assumptions are often valid for applications in deep water ocean areas, they may not be appropriate for shallow water areas, especially in the presence of local shipping activity. Local shipping also produces spatial correlation in the noise and introduces additional complexity for multichannel processing. In this paper, two 30-minute sets of ambient ocean noise, recorded near the San Diego, California coast, are analyzed for stationarity and Gaussianity using the Kolmogorov-Smirnov test. Since processing algorithms based on higher order statistics often assume Gaussianity, time-dependent fluctuations in the third and fourth order cumulants are also analyzed. The analysis reveals significant variability in the time lengths of stationary periods, and episodic periods of nonGaussianity that last for up to five minutes. Statistical fluctuations appear predominantly in the second and fourth order cumulants rather than the third order cumulant. The shipping noise is also shown to be correlated between pairs of hydrophones with the level of correlation varying over time and the correlation ranging from positive to negative with increasing channel separation.

Three-dimensional seismic array characterization study: experiment and modeling.

In the summer of 2003, the Littoral Acoustic Demonstration Center conducted an acoustic characterization experiment for a 21-element marine seismic exploration airgun array of total volume of 0.0588 m(3) (3590 in.(3)). Two Environmental Acoustic Recording System buoys, one with a desensitized hydrophone, were deployed at a depth of 758 m in a water depth of 990 m, near Greens Canyon in the Gulf of Mexico. Shots over a grid were recorded and calibrated to produce absolute broadband (up to 25 kHz) pressure-time dependencies for a wide range of offsets and arrival angles in the water column. Experimental data are analyzed to obtain maximum received zero-to-peak pressure levels, maximum received sound exposure levels, and pressure levels in 13-octave frequency bands for each shot. Experimental data are quantitatively modeled by using an upgraded version of an underwater acoustic propagation model and seismic source modeling packages for a variety of ranges and arrival angles. Experimental and modeled data show good agreement in absolute pressure amplitudes and frequency interference patterns for frequencies up to 1000 Hz. The analysis is important for investigating the potential impact on marine mammals and fish and predicting the exposure levels for newly planned seismic surveys in other geographic areas.

Noise removal and compression using a wavelet transform

Wavelet transforms are a general class of transforms which have had extensive development recently (Daubechies, 1992; Wang and Nguyen, 1996). Finite Fourier transforms are a subset of wavelet transforms, with sines and cosines as the wavelet functions. In this work the use of wavelet transforms for noise removal and the concomitant data compression are examined. This paper shows the application of these techniques first to noisy synthetic data to illustrate the procedures, and then to seismic data.

Sampling requirements and aliasing for higher‐order correlations

While sampling at a Nyquist frequency equal to the highest frequency present in the data (critical sampling) is sufficient to prevent aliasing in both the data and the autocorrelation of a bandlimited energy signal, the sampling requirements for the avoidance of aliasing in higher‐order correlations and spectra are not the same. Also, there is a difference in aliasing effects depending on whether one samples the original continuous‐time signal and calculates the autocorrelation or one samples the continuous‐time autocorrelation. This distinction between sampling procedures must be made for correlations of higher order, as well, for which not only the type of aliasing but also the sampling requirements to prevent aliasing differ. In particular, if one samples the continuous‐time autobicorrelation or autotricorrelation, critical sampling is sufficient to prevent aliasing. In practice, however, it is not usually the continuous‐time autobicorrelation or autotricorrelation that is sampled. Generally, it is the...

Measurements of ambient noise and sperm whale vocalizations in the northern Gulf of Mexico using near bottom hydrophones

The Littoral Acoustic Demonstration Center (LADC) consisting of the University of Southern Mississippi (USM), the University of New Orleans (UNO), and the Naval Research Laboratory at Stennis Space Center (NRL-SSC), with guidance and technical assistance from the Naval Oceanographic Office (NAVOCEANO), was formed to do ambient noise and marine mammal acoustic measurement and analysis. Three Environmental Acoustic Recording System (EARS) buoys, designed and produced by NAVOCEANO, were deployed by LADC in the northern Gulf of Mexico (GoM) in the summer of 2001. These bottom-moored omni-directional hydrophone recording systems were modified by NAVOCEANO to sample almost 12 kHz, so that the vocalizations of sperm whales could be recorded. The Sperm Whale Acoustic Monitoring Program (SWAMP) was conducted during that summer by the Minerals Management Service and its collaborators. The EARS buoys recorded during the entire 36 days of SWAMP from 17 July through 21 August of 2001. The EARS buoy hydrophones, 50m above the bottom, were placed on a downslope line, ending at the largest concentration of sperm whale sightings in the northern GoM, in 600m, 800m, and 1000m water depths. The moorings were instrumented with self-recording environmental sensors to obtain time series data of temperature, conductivity, and pressure at specified depths spanning the water column. Four cruises were made to deploy and recover the buoys and to collect a suite of environmental measurements, including CTD and XBT casts and a chirp sonar survey for bottom properties to support propagation modeling. In between the first and second cruises, Tropical Storm Barry moved through the area and changes in the oceanographic properties were observed. Each EARS buoy recorded a bandwidth of 5859 Hz for 36 days. These data clearly reveals sperm whale vocalizations, passing ships, and seismic airguns. Marine mammal vocalizations and airgun signatures have been isolated and are being analyzed. Spectral levels for ten minute averages of ambient noise on four different days show moderate shipping levels except during the passage of the tropical storm. A plateau in the noise spectrum from 200 to 1000Hz on one day is due to the presence of sperm whales. Spectrograms show sperm whale clicks and creaks and the seismic airgun signal is very clear.