Use Of Cross-correlation Function Research Articles

Quasi-optimal processing simulation of ultrasonic signals

Magnetostrictive level gauges are widely used for measuring the level of bulk material and liquid medium including petroleum products, which determines the relevance of the measurement techniques and level gauges design improvement examination. The research objective is to modify the optimal signal processing classical methods for measuring the time intervals in the magnetostrictive level gauges by using the digital devices with limited computational resources. The article deals with the modification problems of the digital signal processing optimal algorithms providing the real time measuring devices operation. For addressing the challenges, the methods of numerical simulation and statistical processing of ultrasonic signals are used. Digital signal processing quasi-optimal algorithms for calculating the time intervals based on the use of cross-correlation functions leading to the operations number reduction, are described. The represented results can be applied in the level measurement and medicine for electrocardiograms analysis.

Use of Cross-Correlation Function to Study Formation Mechanism of Massive Elliptical Galaxies

AbstractSpatial clustering nature of galaxies has been studied previously through auto correlation function. The same type of cross-correlation function has been used in the present work to investigate parametric clustering nature of galaxies with respect to masses and sizes of galaxies. Here, formation and evolution of several components of nearby massive early type galaxies (M*≥ 1.3 × 1011M⊙have been envisaged through cross-correlations, in the mass-size parametric plane, with high redshift (0.2 ⩽z⩽ 7) ETGs. It is found that the inner most components of nearby ETGs have significant correlation (~ 0.5 ± (0.02–0.07)) with ETGs in the highest redshift range (2 ⩽z⩽ 7) called ‘red nuggets’ whereas intermediate components are highly correlated (~ 0.65 ± (0.03–0.07)) with ETGs in the redshift range 0.5 ⩽z⩽ 0.75. The outermost part has no correlation in any range, suggesting a scenario throughin situaccretion. The above formation scenario is consistent with the previous results obtained for NGC5128 and to some extent for nearby elliptical galaxies after considering a sample of ETGs at high redshift with stellar masses greater than or equal to 108.73M⊙. So the present work indicates a three phase formation instead of two as discussed in previous works.

A new temporal method for the identification of source directions in a reverberant hall

The study presented here is related to the reduction of noise in factory halls. The type of factory hall considered here has large dimensions and contain several industrial machines, running 24 h a day. A method is presented to determine the angular directions which provide the main contributions to the sound levels at any point in the hall. These directions correspond to the sources and their images on the walls and on the obstacles. The method is based on the use of cross-correlation functions of sound signals measured on a microphone array. It is adapted to the constraints of the problem (short measurement time, no possibility to stop the machines, small dimensions of the array, etc.). Experimental results are shown first for several test cases carried out in a semi-anechoic room and in a rectangular room, and, then, for the case of a surface-planing machine in a cluttered hall.

Identification of Nonlinear Mechanical Systems by Use of Volterra Kernels.

Many classes of nonlinear systems can be represented by Volterra kernels. One of the authors has proposed a method for obtaining the Volterra kernels by use of M-sequences and cross-correlation function. In this paper, the authors propose a new method for identification of nonlinear mechanical systems by use of Volterra kernels. The nonlinear mechanical systems are approximated to a combination of a linear system and its square and cubic portion. Then, the parameters, which represent the relative maginitude of the square and cubic part, are calculated by use of the crosscorrelation function. In order to show that nonlinear mechanical systems can be identified by the parameters, computer simulations are carried out. The nonlinear mechanical system simulated consists of a DC servo motor and 1-link arm. From the results of simulations, it is shown that the nonlinear mechanical system can be identified by the proposed method.

The use of cross-correlation functions in the analysis of circular dichroism spectra

Following Gordon, we show that the circular dichroism (CD) spectrum is proportional to the imaginary part of the Fourier transform of the cross-correlation function of the electric dipole moment and of the magnetic dipole moment. Such a result is useful in the study of CD band shapes, and also in obtaining a spectrum from a classical trajectory calculation, as was done for absorption by Noid, Koszykowski, and Marcus. For ergodic and multiperiodic regimes, the formula reduces to the Fourier cross spectrum of the two moment functions. As an application, we have run classical trajectories calculations for two coupled CH stretchings belonging to a chiral HCCH fragment, in the fixed partial charge approximation. Two sets of results are presented, relative to low and high total energy: Comments are made about the spectroscopic manifestation of normal, local, and chaotic modes.

Spatial variability of infiltration in a semi-arid environment

Fifty-two double-ring infiltrometer tests, performed in a small, partly urbanized catchment in northern Tunisia are analyzed. Spatial variability is characterized by use of cross-correlation functions. Spatial patterns of infiltration properties are shown to be governed by geomorphology and occurring vegetation. Different geomorphological zones and zones with equal density of vegetation tend to be oriented in a parallel pattern in relation to the wadi. Statistical properties of infiltration capacities depending on geomorphological zone are presented.

The use of cross-correlation function for the alignment of ECG waveforms and rejection of extrasystoles

The cross-correlation function for alignment of ECG waveforms and rejection of artifacts was studied. ECG waveforms were recorded and digitized (10-bit resolution) at 1.28 KHz and were processed with a CDC 6600 computer. The cross-correlation function was calculated using the cross spectrum and the fast Fourier transform algorithm. The maximum value of the cross-correlation function and the time location of that value were searched for (a) the similarity between the waveforms (for elimination of extrasystoles), and (b) measuring the relative time delay (for the waveform's alignment in the averaging process) between the ECG waveforms. Prior to the correlation procedure each of the ECG waveforms was filtered through a nonrecursive digital bandpass filter. Experiments with various filters indicated that when low-frequency cutoff at 30 Hz and high-frequency cutoff at 250 Hz were used the maximum value of the cross-correlation function was higher than 0.9 for most of our recorded waveforms and more accurate results were obtained.

Local modes and cross-correlation functions

It is shown how the use of cross-correlation functions and their Fourier transforms provides a convenient probe of the division of the classical phase space for stretching vibrations of H2O into local, normal, and stochastic fractions. Resulting classical estimates for the numbers of total and local states, N(E) and Nl(E), respectively, as functions of energy are in excellent agreement with previous quantal and semiclassical results. The classical estimate of the number of stochastic states Ns(E) as a function of energy is a new result. The present method is readily generalizable to polyatomic molecules with many vibrational degrees of freedom.