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DETECTION OF OSCILLATORY AND IMPULSIVE TRANSIENTS USING HIGHER-ORDER CORRELATIONS AND SPECTRA

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 1992年第5期91卷 2763-2776页

作者： PFLUG, LA IOUP, GE IOUP, JW BARNES, KH FIELD, RL RAYBORN, GH UNIV NEW ORLEANS DEPT PHYSNEW ORLEANSLA 70148 UNIV SO MISSISSIPPI DEPT PHYS & ASTRONHATTIESBURGMS 39406

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 noise. Rectification as part of the detection process improves the performance of the bicorrelation detector and also places the peak of maximum magnitude at the origin. This eliminates the problem in detection or time delay estimation that the existence of multiple peaks due to symmetries in the auto-bicorrelation or the bicorrelation of repeated signals may cause. The tricorrelation detector also performs better with rectification than without. For an unknown source, the bicorrelation and tricorrelation detectors with rectification perform on a level comparable to the cross-correlation detector for certain signals. Comparisons are made between repeating a known source and repeating noisy received signals in the bicorrelation.

关键词： Rectification probability density functions

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ENVELOPE STATISTICS OF PARTIALLY SATURATED PROCESSES

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 1982年第1期72卷 151-158页

作者： MIKHALEVSKY, PN USN CTR UNDERWATER SYSTNEW LONDONCT 06320

The probability density functions associated with the envelope and phase of a partially saturated process are derived. The derivation assumes that the single path phases are Gaussian random variables with arbitrary means but with identical variances σ² _?. The analysis also includes the effects of Gaussian noise on the statistics. It is shown that in the limit as the standard deviation of the single path phases becomes large (?π/2), the densities approach previously derived results for fully saturated phase random propagation. In the limit as σ_?→0, the densities for unsaturated propagation, namely constant signal plus Gaussian noise, are recovered. The results derived are used for determining the distributions of fades and receiver operating characteristics for a partially saturated process. The fading probability and the signal‐to‐noise ratio required to detect the partially saturated signal is directly proportional to σ_?.

关键词： Acoustic noise measurement Noise propagation probability density functions Statistical analysis Statistical properties

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IDENTIFICATION OF STRUCTURAL PARAMETERS USING LOW-AMPLITUDE IMPULSIVE LOADING

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 1975年第5期57卷 1128-1137页

作者： SWEET, AL SCHIFF, AJ KELLEY, JW PURDUE UNIV SCH IND ENGNW LAFAYETTEIN 47907 PURDUE UNIV SCH MECH ENGNW LAFAYETTEIN 47907 PURDUE UNIV SCH AERONAUT & ASTRONAUTW LAFAYETTEIN 47907

A parameter‐estimation procedure is developed using the average of the response of a structure to a sequence of impulsive force loadings. The finite Fourier sine and cosine transforms of the averaged response are computed. using a mathematical model of a linear one‐degree‐of‐freedom system, whose acceleration response has normal uncorrelated noise added to it, the joint probability density function of the Fourier coefficients is found. Applying the principle of maximum likelihood, estimates for the percent of critical damping, the natural frequency, and the magnitude of the impulse are computed using Marquardt’s method. Data were generated by digital simulation, analog simulation, and by exciting an experimental model. The resulting estimates and their confidence intervals are shown in tabular form. Error analysis due to random impulsive forces, finite pulse width of the force loading, and correlation of the noise are performed. The technique can be used in estimating the damping of systems in which the response to impulsive loading can be measured but is small relative to the ambient response. Subject Classification: 45.40; 40.35.

关键词： Error analysis Fourier transforms probability density functions

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A probabilistic method for online treatment plan modification

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MEDICAL PHYSICS 2005年第6期32卷 1930-1930页

作者： Flynn, R Jeraj, R Mackie, T Univ Wisconsin Madison WI USA

Purpose: To develop an IMRT treatment planning method that accounts for increased knowledge of tumor and normal tissue location gained from inter- or intra-fractional imaging. Method and Materials: Knowledge of tumor location in each fraction or sub-fraction is represented by a probability density function (pdf), p(n,n′,t) , that describes the probability that a voxel at index n in the planning image will be located at voxel n ′ at a later time t . The pdf is changing as the new information becomes available. A set of beam profiles for each fraction or sub-fraction is then obtained by minimizing the quadratic objective function by accounting for probabilistic nature of the beamlet dose distribution: in each fraction. This optimization problem is set with the intention that the beamlets that have the highest risk of missing the tumor will not be delivered until adequate knowledge of tumor location becomes available. We apply this method to a case of a disk-shaped tumor inside a disk-shaped phantom with a tomotherapy beam geometry. Results: The method proved to deliver more conservative dose distributions at the beginning of treatment than at the end for both inter- and intra-fractional cases. For early fractions and sub-fractions, low-risk doses were delivered to regions where the probability was high that the tumor would be present during the treatment. As knowledge of tumor location improved, the remaining dose at the periphery of the tumor was filled-in. Conclusion: We showed that incorporating increased knowledge about tumor and normal tissue location, obtained by repeatitive on-line imaging leads to superior treatment plans.

关键词： Cancer Medical imaging Medical treatment planning Tissue engineering Intensity modulated radiation therapy probability density functions

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OUTPUT probability DISTRIBUTION OF A CORRELATION DETECTOR WITH SIGNAL-PLUS-NOISE INPUTS

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 1963年第7期35卷 1041-&页

作者： JACOBSON, MJ Rensselaer Polytechnic Institute Troy New York

In this paper, a study is made of the problem of determining the probability density function of the output of a correlation detector whose two inputs consist of correlated signal corrupted by uncorrelated noise. The inputs are stationary and Gaussian, one having the characteristics of white noise and the other being RC‐filtered white noise. The postmultiplier averager is also an RC filter. The general case of signal‐plus‐noise inputs is investigated, and the special cases of signal‐only and noise‐only inputs are also considered. Detailed results are presented when the ratio of the time constant of the postmultiplier filter to that of the premultiplier filter is 1 2 and also in the practical case when this ratio is large. With the probability distribution determined, a statistical theory of signal detection is applied, a major result being the determination of the relationship between detection probability and the classical detection measure, output signal‐to‐noise ratio.

关键词： probability theory Random noise probability density functions Statistical analysis

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NEW MODELS ON THE OCEAN ACOUSTIC DETECTION PROCESS

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 1981年第6期69卷 1724-1734页

作者： PSARAFTIS, HN PERAKIS, AN MIKHALEVSKY, PN USN CTR UNDERWATER SYSTNEW LONDON LABNEW LONDONCT 06320

The basic problem of the ocean acousticdetection process is formulated analytically under the assumption of fully developed saturated phase random multipath acoustic fluctuations. Detection is defined as occurring whenever ρ, the root‐mean‐square pressure at the receiver, exceeds a specified threshold level ρ₀. Two models, one exact and one approximate, are developed for obtaining the probability density functions of the time between two successive detections and of the time ρ is above ρ₀ (holding time). The two models are compared with one another and with the extensively used (λ, σ) model. One of the reasons that the latter model has a limited success in practice is the inability to estimate the appropriate value for λ, a parameter which is determined empirically. In this paper we have derived an appropriate value for λ, in terms of ν (the single path root‐mean‐square phase rate), σ² ₁ (half the long time average mean‐square pressure at the receiver) and ρ₀ (the threshold level). Using this equivalent value for λ, we observe that our exact and approximate detectionmodels exhibit similar long‐term behavior but markedly different short‐term characteristics as compared with the (λ,σ) model. This is due to the memory of the process, a property that cannot be accounted for in the (λ,σ) model. A comparison of these models with data obtained from various field experiments demonstrates, in most cases, an improved capability over the (λ,σ) model.

关键词： Acoustic sensing Ocean acoustics Acoustic modeling Experiment design probability density functions

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STATISTICS OF ONE-DIMENSIONAL CLUSTER MOTION

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JOURNAL OF CHEMICAL PHYSICS 1977年第2期67卷 781-792页

作者： WRIGLEY, JD REED, DA EHRLICH, G UNIV ILLINOIS COORDINATED SCI LABURBANAIL 61801 UNIV ILLINOIS DEPT METURBANAIL 61801 UNIV ILLINOIS DEPT PHYSURBANAIL 61801

The statistics of clusters, made up of metal atoms in adjacent one‐dimensional diffusion channels, are developed quantitatively. Kolmogorov’s equation is used to find the mean square displacement for clusters capable of existing in energetically different configurations at the same position of the center of mass; this is done under steady state conditions, for which the probability of finding a specified configuration does not vary in time. Two systems are examined: (1) dimers capable of existing in an infinite number of states, a situation realized if dissociation is allowed, and (2) trimers diffusing on planes, such as W(211), on which nine distinct jump processes may contribute to the cluster motion. In dimer diffusion it is demonstrated that dissociation may be important even if the fraction dissociated is minor. For trimers, previous attempts to approximate the motion through the use of average transition rates are compared with the exact solutions and found wanting. Important statistical quantities beyond the mean square displacement are presented for simple dimers capable of existing in only two states. The generating function is derived, together with the higher moments of the displacement. probability density functions for the number of jumps in an interval t, for the waiting time up to a specified jump, as well as for the displacements are all presented. These differ significantly from the density functions for an ordinary random walk. However, an averaging technique allows simple approximations for the behavior of dimers.

关键词： Diffusion Dissociation Exact solutions probability density functions Random walks

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SPEECH AMPLITUDE STATISTICS AND THE GAMMA-density FUNCTION AS A THEORETICAL APPROXIMATION

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 1986年第6期80卷 1583-1588页

作者： NIEDERJOHN, RJ HAWORTH, DG Department of Electrical Engineering and Computer Science Marquette University Milwaukee Wisconsin 53233

Knowledge of the speech amplitude density provides basic data concerning the statistics of the continuous speech waveform. The objective of this paper is to present data which characterize the longtime speech amplitude density utilizing a data base of sufficient size to describe the distribution. The data base consists of approximately 45 min of recorded speech for each of the 25 speakers. Two parameters of a theoretical gamma density function are estimated from the experimental data to provide the best curve fit between the experimental data and the gamma density function. Overall results presented in this paper substantiate three main conclusions: (a) There is a significant difference between the speech amplitude density for male and female speakers; (b) the speech amplitude density for positive speech amplitudes differs from that for negative speech amplitudes; and (c) the gamma probability density function is a better approximation for full‐wave rectified speech than it is when considering just positive or just negative amplitudes.

关键词： Speech density functional theory Real functions probability density functions Statistical analysis

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STATISTICAL DISTRIBUTION OF FREE PATH-LENGTHS IN THE ACOUSTICS OF ENCLOSURES

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 1984年第5期75卷 1519-1521页

作者： BENEDETTO, G SPAGNOLO, R Istituto Elettrotecnico Nazionale Galileo Ferraris corso Massimo d’Azeglio 42 Torino Italy

In the acoustics of enclosures it is often necessary to know the probability density function of free pathlengths. Some applications are reported of Coleman’s formula for the exact computation of the distribution and moments in ergodic regular enclosures. The results are compared with those obtained by computer ray‐tracing simulation in the case of the specular reflection law. It is shown that the distribution is strictly connected to the shape of the enclosure.

关键词： Computer simulation probability density functions Statistical distribution

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IONIC-CONDUCTION IN ONE DIMENSION - A STRUCTURAL STUDY OF THE HOLLANDITE K1.54MG0.77TI7.23O16 OVER THE RANGE 133 LESS-THAN-OR-EQUAL-TO T LESS-THAN-OR-EQUAL-TO 919K

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JOURNAL OF CHEMICAL PHYSICS 1986年第1期85卷 475-484页

作者： WEBER, HP SCHULZ, H MAX PLANCK INST FESTKORPERFORSCH HEISENBERGSTR 1D-7000 STUTTGART 80FED REP GER

Joint probability density functions (pdf) of the mobile K atom (and their corresponding pseudopotentials) have been obtained from seven x‐ray (M o K α) intensity data sets collected on a one‐dimensional conductor w... 详细信息

Joint probability density functions (pdf) of the mobile K atom (and their corresponding pseudopotentials) have been obtained from seven x‐ray (M o K _α) intensity data sets collected on a one‐dimensional conductor with the hollandite structure (K_1.54Mg_0.77Ti_7.23O₁ ₆; space group I4/m; Z=1). The data were collected at high resolution [(sin?θ/λ)_max ≥0.9 ?^? ¹] and at several temperatures (133, 298, 387, 459, 540, 707, and 919 K) in order to determine the conduction mechanism. Two models of the K distribution within the strand of cavities making up the conduction tunnel have been refined. In the most complex model B [R _w(F) =0.02], up to four atomic positions are needed to describe the observed electron density. The pdfs show that—already at room temperature and within undamaged segments of the conduction tunnel—potassium ions diffuse at a high rate across the bottleneck between two neighboring cavities. Below about 430 K the potassium ions preferentially occupy sites shifted off the cavity center in the direction of the bottleneck; above this temperature the cavity center becomes the preferred location. At 298 K the potential barrier at the bottleneck amounts to 0.032(4) eV. In a plot of the cell constants vs T an inflection shows up at 3873 ₃ (refined from the one‐atom model A) vs T. A comparative study of two other hollandites K_1.92V₈O₁ ₆ and (Ba_0.98Ca_0.03 Zr_0.02) [Al_1.1Ni_0.48 Ti_6.4] with different tunnel stoichiometry underscores the importance of the values of ionic density and charge in the conduction column to the conductivity.

关键词： Ionic conduction probability density functions Data sets Magnesium Nickel

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