The effects of random noise on optically determined autocorrelation and chord functions

Global chord functions are good candidates for use in an autonomous shape recognition system because not only do they possess the valuable attributes of being practically invariant to scaling, translation and rotation but it is possible to determine them very rapidly, by the autocorrelation method, in a hybrid optical-digital system. A further aspect must however be examined before implementation in an operational system is considered; the robustness of the complete processing to random noise. In this paper the effects of additive uncorrelated noise in the input image on the autocorrelation and the resulting chord functions are addressed. It is shown that the whole process is quite robust. Most of the chord function structure is retained for signal to noise ratios of 2:1 and some is still present at 1:1.     

Neural network processing for adaptive line enhancement

This paper describes the inverstigation devoted to establish suitable weights in a feed-forward neural network realizing the narrow-band filtering map in the case of adaptive line enhancement(ALE) by the utility of the optimum common learning rate back propagation (OCLR BP) algorithm. It is found that a feed-forward network with 64 linear input and output neurons, and 8 odd sigmoid neurons in the hidden layer, i.e. an (64→8→64) architecture, could establish the specific input-output function in the case of relatively low signal-to-noise radio. Only is an input signal consisting of mixed periodic and broad-band components available to the network system. After learning, both the "fanning-in-connection patterns", each of which consists of weights fanning into a hidden-neuron From all the outputs of input-neurons, and the "fanning-out-connection patterns", each of which consists of weights fanning out from a hidden-neuron to all the inputs of output-neurons, are tuned to the periodic signals. The nonline     

Time-oscillating Lyapunov modes and the momentum autocorrelation function

The Lyapunov vectors corresponding to the steps of Lyapunov spectra for many-particle systems show time-oscillating behavior in two types of Lyapunov modes, one associated with time-translational invariance and the other with spatial translational invariance. Our result is that, for each coordinate direction, the longest period of the Lyapunov modes is twice as long as the period of the momentum autocorrelation function. A simple explanation for this relation is proposed and we argue that this result is generally true for many-particle systems. This gives the first quantitative connection between the Lyapunov modes and an experimentally accessible quantity.     

利用螺旋型波带片进行边缘增强成像

为了提高对等离子体内界面区域的诊断精度,研究了利用螺旋型波带片实现边缘增强成像的技术。制作了用于可见光波段的一阶螺旋型波带片,最外环宽度3μm。利用螺旋型波带片对振幅式物体进行了边缘增强成像,实验获得了成像物体内边界区域的清晰图像,界面区域的成像强度得到很大增强。通过实验测量发现,当物距在菲涅耳衍射区域内时,螺旋型波带片也能够获取较好的成像质量,表明螺旋型波带片具有较大的视场角,能够对大尺度物体进行边缘成像。基于螺旋型波带片的边缘增强成像可以弥补传统成像方式对界面区域成像的不足,提高对等离子体内界面区域的诊断能力。     

利用螺旋型波带片进行边缘增强成像

为了提高对等离子体内界面区域的诊断精度,研究了利用螺旋型波带片实现边缘增强成像的技术。制作了用于可见光波段的一阶螺旋型波带片,最外环宽度3 μm。利用螺旋型波带片对振幅式物体进行了边缘增强成像,实验获得了成像物体内边界区域的清晰图像,界面区域的成像强度得到很大增强。通过实验测量发现,当物距在菲涅耳衍射区域内时,螺旋型波带片也能够获取较好的成像质量,表明螺旋型波带片具有较大的视场角,能够对大尺度物体进行边缘成像。基于螺旋型波带片的边缘增强成像可以弥补传统成像方式对界面区域成像的不足,提高对等离子体内界面区域的诊断能力。     

Velocity autocorrelation function of a Brownian particle

In this article, we present molecular dynamics study of the velocity autocorrelation function (VACF) of a Brownian particle. We compare the results of the simulation with the exact analytic predictions for a compressible fluid from [T.S. Chow, J.J. Hermans, Physica 65, 156 (1973)] and an approximate result combining the predictions from hydrodynamics at short and long times. The physical quantities which determine the decay were determined from separate bulk simulations of the Lennard-Jones fluid at the same thermodynamic state point. We observe that the long-time regime of the VACF compares well the predictions from the macroscopic hydrodynamics, but the intermediate decay is sensitive to the viscoelastic nature of the solvent.     

The autocorrelation function of a pseudointegrable system

The autocorrelation function of a pseudointegrable system is considered. The system consists of “billiards” on plane surface formed out of three squares arranged in an “L” shape. This system has the important property of being constructed from copies of an integrable subsystem, the single square. The motion can be decomposed into a continuous and a discrete part, the unpredictability in the system being associated with the latter. A discrete autocorrelation function is calculated, and its decay properties investigated. Structure found in this autocorrelation function is associated with the continued fraction expansion of the ratio of velocity components. For repeating continued fractions, such as the golden mean, the autocorrelation function exhibits a selfsimilar structure. For the general case of a randomly chosen velocity ratio, we derive the time dependence of the number of occurences of “large” autocorrelation values, which differs from the behavior in integrable and chaotic systems.     

Analytical expressions for momentum autocorrelation function of a classic diatomic chain

We use recurrence relations method to study a classical harmonic diatomic chain. The momentum autocorrelation function results from contributions of acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical branches are derived as even-order Bessel function expansions. The expansion coefficients are given in terms of integrals of real and complex elliptic functions for the acoustic and optical branches, respectively. Double convolution results respectively in integrals of trigonometric and hyperbolic functions for expansion coefficients of acoustic and optical branches.     

Complex singularities of the fluid velocity autocorrelation function

There are intensive debates regarding the nature of supercritical fluids: if their evolution from liquid-like to gas-like behavior is a continuous multistage process or there is a sharp well-defined crossover. Velocity auto-correlation function Z is the established detector of evolution of fluid particles dynamics. Usually, complex singularities of correlation functions give more information. For this reason, we investigate Z in complex plane of frequencies using numerical analytic continuation. We have found that naive picture with few isolated poles fails describing Z(ω) of one-component Lennard-Jones (LJ) fluid. Instead, we see the singularity manifold forming branch cuts extending approximately parallel to the real frequency axis. That suggests LJ velocity autocorrelation function is a multivalued function of complex frequency. The branch cuts are separated from the real axis by the well-defined “gap” whose width corresponds to an important time scale of a fluid characterizing crossover of system dynamics from kinetic to hydrodynamic regime. Our working hypothesis is that the branch cut origin is related to competition between one-particle dynamics and hydrodynamics. The observed analytic structure of Z is very stable under changes in the temperature; it survives at temperatures two orders of magnitude higher than the critical one.     

Short time behavior of the velocity autocorrelation function

A systematic method for evaluating velocity correlation functions of a hard sphere fluid for short times is presented The complete contributions ～ t and t² are obtained, formally valid for all densities.     

Calculation of a "narrowed" autocorrelation function

A method of calculating an autocorrelation function with extremely narrow peaks is described. This is done by including terms in the autocorrelation expression corresponding to delays at 2 tau, 3 tau, etc., in addition to the usual term with delay tau. Implications in the frequency domain are explored. Graphs of this autocorrelation function for a number of violin sound samples, including a two-octave scale, vibrato, and glissando, are presented. Graphs of the autocorrelation function for some synthetic sound samples are also included.     

一种基于自相关函数的幂律检测器

针对水下高斯噪声中非高斯瞬态信号的检测问题,在研究Nuttall提出的power-law(幂律)检测器的基础上,为了提高其检测性能,依据信号和噪声的自相关函数的差异,提出了基于自相关函数的power-law检测器,并对其参数的最佳选取及检测性能进行了仿真研究。仿真结果表明,基于自相关函数的检测器较基于DFT的power-law检测器性能有所提高,有一定的可行性。     

The non-exponential behavior of the velocity autocorrelation function

The contribution to the velocity autocorrelation function from ring events is studied for low densities and t?2t₀ using a kinetic model. Agreement with computer experiments for $\text{V}\text{V}{}_0\text{= 18}$ is found to be good.     

A memory function model for the velocity autocorrelation function and the self-diffusion coefficient in simple dense fluids

A memory-function model is used to compute the velocity autocorrelation function and the self-diffusion coefficient of a dense Lennard-Jones fluid from the zero-time correlation functions of the molecular velocity and its first two time derivatives. It is shown that these zero-time correlation functions can be evaluated in terms of the radial distribution function and the pair potential only, i.e. without considering higher order correlation functions. Since molecular dynamics results are available for the radial distribution function as well as the velocity autocorrelation function and the self-diffusion coefficient, a rigorous test of the chosen memory function is possible. The agreement is reasonable, although generally not within the error bands of the molecular dynamics results.     

The sample autocorrelation function and the detection of long-memory processes

The detection of long-range dependence in time series analysis is an important task to which this paper contributes by showing that whilst the theoretical definition of a long-memory (or long-range dependent) process is based on the autocorrelation function, it is not possible for long memory to be identified using the sum of the sample autocorrelations, as usually defined. The reason for this is that the sample sum is a predetermined constant for any stationary time series; a result that is independent of the sample size. Diagnostic or estimation procedures, such as those in the frequency domain, that embed this sum are equally open to this criticism. We develop this result in the context of long memory, extending it to the implications for the spectral density function and the variance of partial sums of a stationary stochastic process. The results are further extended to higher order sample autocorrelations and the bispectral density. The corresponding result is that the sum of the third order sample (auto) bicorrelations at lags h,k≥1$h,k\ge 1$, is also a predetermined constant, different from that in the second order case, for any stationary time series of arbitrary length.     

Clipped time autocorrelation function of intensity fluctuations for a non gaussian field

Numerical results for the single and double clipped autocorrelation functions of intensity fluctuations of squared intensity of gaussian-exponential field are reported and compared with the unclipped ones.     

Psychophysical evidence against the autocorrelation theory of auditory temporal processing.

Nowadays, it is widely believed that the temporal structure of the auditory nerve fibers' response to sound stimuli plays an important role in auditory perception. An influential hypothesis is that information is extracted from this temporal structure by neural operations akin to an autocorrelation algorithm. The goal of the present work was to test this hypothesis. The stimuli consisted of sequences of unipolar clicks that were high-pass filtered and mixed with low-pass noise so as to exclude spectral cues. In experiment 1, "interfering" clicks were inserted in an otherwise periodic (isochronous) click sequence. Each click belonging to the periodic sequence was followed, after a random portion of the period, by one interfering click. This disrupted the detection of temporal regularity, even when the interfering clicks were 5 dB less intense than the periodic clicks. Experiments 2-4 used click sequences that showed a single peak in their autocorrelation functions. For some sequences, this peak originated from "first-order" temporal regularities, that is from the temporal relations between consecutive clicks. For other sequences, the peak originated instead from "second-order" regularities, relative to nonconsecutive clicks. The detection of second-order regularities appeared to be much more difficult than the detection of comparable first-order regularities. Overall, these results do not tally with the current autocorrelation models of temporal processing. They suggest that the extraction of temporal information from a group of closely spaced spectral components makes no use of time intervals between nonconsecutive peaks of the amplitude envelope.     

The exact velocity autocorrelation function of a model system

The velocity autocorrelation function of a particle in a model system with realistic diffusion is calculated exactly and compared with the corresponding result in the one-dimensional case. The method employed yields the result of Lebowitz and Sykes in one dimension in a very simple manner.Research Supported by NSF Grant No. R019881001.     

The velocity autocorrelation function of a finite model system

We investigate in detail the dependence of the velocity autocorrelation function of a one-dimensional system of hard, point particles with a simple velocity distribution function (all particles have velocities ±c) on the size of the system. In the thermodynamic limit, when both the number of particlesN and the length of the boxL approach infinity andN/L , the velocity autocorrelation function(t) is given simply by c² exp(–2ct@#@). For a finite system, the function _N(t) is periodic with period 2L/c. We also show that for more general velocity distribution functions (particles can have velocities ±c_i,i = 1,...), _N(t) is an almost periodic function oft. These examples illustrate the role of the thermodynamic limit in nonequilibrium phenomena: We must keept fixed while letting the size of the system become infinite to obtain an auto-correlation function, such as(t), which decays for all times and can be integrated to obtain transport coefficients. For any finite system, our _N (t) will be very close to(t) as long ast is small compared to the effective size of the system, which is 2L/c for the first model.Supported in part by the AFOSR under Contract No. F44620-71-C-0013.     

Edge adaptive image resolution enhancement in video sensor network

Video sensor network usually uses fairly low-resolution images due to the limited transmission bandwidth in transmitting images. It is potential to enhance the captured low-resolution images using image resolution enhancement technique that is able to produce a high-resolution image from its low-resolution counterpart. The key challenge of image resolution enhancement is to preserve the edge structure in images. In this paper, a new image resolution enhancement approach is proposed to estimate the intensity of the unknown pixel using a bilateral weighted average of that of its neighboring pixels. More specifically, the neighboring pixels with nearer distance have larger contributions. Furthermore, the neighboring pixels belonging to direction with smaller variation have larger contributions. Experimental results are provided to show that the proposed approach outperforms several conventional edge-directed image interpolation algorithms. Furthermore, the proposed approach yields low computational complexity; it is potential for real-time implementation.