Use Of Autocorrelation Research Articles

Experimental study on phase compensation method based on autocorrelation in laser heterodyne detection

Spatial distortion phase seriously deteriorates the performance of heterodyne detection system. Effective phase compensation is necessary to reduce the impact of the distortion phase. Compared with the compensation method based on the combination of an optimization algorithm and sequence shifting, that by use of autocorrelation does not require repetitive iterations and avoids false alarms, resulting in better stability and real-time properties. In this paper, the distortion phase is generated by an atmospheric turbulence simulator to examine the performance of the new compensation method. The experiment results show that compared with the single point detector method, the new method can even increase the SNR by 50.3 dB, which confirms the effectiveness of the compensation method. Due to easy implementation and excellent performance, it is possible that the new method will become a universal means to compensate for the spatial distortion phase in the heterodyne detection.

Comparative analysis of speech coders

In this paper a comparative analysis of some of the most popular speech coders is presented. Qualitatively and quantitatively are tested Linear Prediction Coding in its implementation LPC-10e and with the use of auto-correlation and covariance,

Experimental Investigations of Time-Delay Signature Concealment in Chaotic External Cavity VCSELs Subject to Variable Optical Polarization Angle of Feedback

Time-delay (TD) signature concealment in a chaotic vertical-cavity surface-emitting laser (VCSEL) is studied experimentally. The VCSEL is subject to variable optical polarization angle of feedback along with variable optical feedback strength and bias current. The TD signature concealment is determined through the use of autocorrelation and information theory-based permutation entropy functions. It is found that the TD signature is concealed at low feedback of strength of order -18 dB. At moderate feedback strength, the TD signature is sensitive to the rotation of optical polarization angle of feedback with TD concealment being observed for polarization angles in the range from 45° to 90°.

Autocorrelation analysis of military jet aircraft noise

Jet noise research has seen increased use of autocorrelation analyses to glean physical insight about the source and its radiation properties. Length scales and other features have been identified in support of models incorporating large-scale (LSS) and fine-scale (FSS) turbulent structures. In this paper, the meaningful use of autocorrelation in jet noise analysis is further examined. A key finding is that the effect of the peak frequency on autocorrelation width needs to be removed prior to making conclusions about the relative LSS and FSS contributions. In addition, the Hilbert transform is applied to create an envelope of the autocorrelation function to more consistently define a characteristic time scale. These methods are first applied to the analytical LSS and FSS similarity spectra, previously developed by Tam et al. [AIAA 96-1716, 1996]. It is found that the envelope of the FSS similarity autocorrelation function is more similar to that of a delta function than the LSS envelope. These curves are used to more effectively quantify FSS and LSS features in noise spectra from the F-22A Raptor. [Work supported by ONR.]

Ground structure imaging by inversions of Rayleigh wave ellipticity: sensitivity analysis and application to European strong-motion sites

The knowledge of the local soil structure is important for the assessment of seismic hazards. A widespread, but time-consuming technique to retrieve the parameters of the local underground is the drilling of boreholes. Another way to obtain the shear wave velocity profile at a given location is the inversion of surface wave dispersion curves. To ensure a good resolution for both superficial and deeper layers, the used dispersion curves need to cover a wide frequency range. This wide frequency range can be obtained using several arrays of seismic sensors or a single array comprising a large number of sensors. Consequently, these measurements are time-consuming. A simpler alternative is provided by the use of the ellipticity of Rayleigh waves. The frequency dependence of the ellipticity is tightly linked to the shear wave velocity profile. Furthermore, it can be measured using a single seismic sensor. As soil structures obtained by scaling of a given model exhibit the same ellipticity curve, any inversion of the ellipticity curve alone will be ambiguous. Therefore, additional measurements which fix the absolute value of the shear wave velocity profile at some points have to be included in the inversion process. Small-scale spatial autocorrelation measurements or MASW measurements can provide the needed data. Using a theoretical soil structure, we show which parts of the ellipticity curve have to be included in the inversion process to get a reliable result and which parts can be omitted. Furthermore, the use of autocorrelation or high-frequency dispersion curves will be highlighted. The resulting guidelines for inversions including ellipticity data are then applied to real data measurements collected at 14 different sites during the European NERIES project. It is found that the results are in good agreement with dispersion curve measurements. Furthermore, the method can help in identifying the mode of Rayleigh waves in dispersion curve measurements.

Examining the Gain in Model Prediction Accuracy Using Serial Autocorrelation for Dominant Height Prediction

Abstract Within-subject serial correlation (autocorrelation) has long been a concern in forest growth and yield modeling but has been ignored for predictive purposes in most studies. In this study, we used linear prediction theory combined with linearized (with respect to random effects) nonlinear mixed models to investigate the improvement in model prediction achieved with autocorrelation. In this setting, predictions rely on estimates of common parameters obtained from a set of previous growth series and prior observations of new growth series, allowing the response variable for the new series to be projected either backward or forward in time. The prediction gains associated with using autocorrelation were evaluated using stem analysis data sets for black spruce (Picea mariana [Mill.] BSP) and red alder (Alnus rubra Bong.). The evaluations involved splitting the data and comparing models with one or more random parameters, with and without use of autocorrelation. Autocorrelation improved the projection of dominant height (site index) over short ranges (10–20 years), but the gain was trivial for the long range (>20 years). Consequently, in cases of dominant height projection based on one single observation, for practical purposes, autocorrelation can be ignored in both model-fitting and prediction stages. Cross-comparison between models with different random effects indicated that simple models with one random effect had the best predictive performance. Rather than excluding such models solely on the basis of certain fit statistics, it is recommended that the predictive abilities of models with a single random effect be evaluated, with and without correlated errors, relative to their counterparts with more random effects.

Use of autocorrelation of wavelet coefficients for fault diagnosis

This paper presents a novel time–frequency-based feature recognition system for gear fault diagnosis using autocorrelation of continuous wavelet coefficients (CWC). Furthermore, it introduces an original mathematical approximation of gearbox vibration signals which approximates sinusoidal components of noisy vibration signals generated from gearboxes, including incipient and serious gear failures using autocorrelation of CWC. First, the drawbacks of the continuous wavelet transform (CWT) have been eliminated using autocorrelation function. Secondly, the autocorrelation of CWC is introduced as an original pattern for fault identification in machine condition monitoring. Thirdly, a sinusoidal summation function consisting of eight terms was used to approximate the periodic waveforms generated by autocorrelation of CWC for normal gearboxes (NGs) as well as occurrences of incipient and severe gear fault (e.g. slight-worn, medium-worn, and broken-tooth gears). In other words, the size of vibration signals can be reduced with minimal loss of significant frequency content by means of the sinusoidal approximation of generated autocorrelation waveforms of CWC as reported in this paper.

The adaptive augmented GMRES method for solving ill-posed problems

The GMRES method is an iterative method that provides better solutions when dealing with large linear systems of equations with a non-symmetric coefficient matrix. The GMRES method generates a Krylov subspace for the solution, and the augmented GMRES method allows augmentation of the Krylov subspaces by a user supplied subspace which represents certain known features of the desired solution. The augmented GMRES method performs well with suitable augmentation, but performs poorly with unsuitable augmentation. The adaptive augmented GMRES method automatically selects a suitable subspace from a set of candidates supplied by the user. This study shows that this method maintains the performance level of augmented GMRES and lightens the burden it puts on its users. Numerical experiments compare robustness as well as the efficiency of various heuristic strategies. References M. L. Baart. The use of auto-correlation for pseudo-rank determination in noisy ill-conditioned linear least-squares problems. IMA Journal of Numerical Analysis, 2:241--247, 1982. doi:10.1093/imanum/2.2.241 J. Baglama and L. Reichel. Augmented GMRES-type method. Numerical Linear Algebra with Applications, 14:337--350, 2007. doi:10.1002/nla.518 D. Calvetti, B. Lewis, and L. Reichel. GMRES-type methods for inconsistent systems. Linear Algebra and its Applications, 316:157--169, 2000. doi:10.1016/S0024-3795(00)00064-1 D. Calvetti, B. Lewis, and L. Reichel. On the choice of subspace for iterative methods for linear discrete ill-posed problems. Int. J. Appl. Math. Comput. Sci, 11:1069--1092, 2001. http://www.math.kent.edu/ reichel/publications/subspaceselect.pdf G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins University Press, 2nd edition, 1989. P. C. Hansen. Regularization tools: A matlab package for analysis and solution of discrete ill-posed problems. Numerical Algorithms, 6:1--35, 1994. doi:10.1007/BF02149761 P. C. Hansen. Rank Deficient and Discrete Ill-Posed Problems. SIAM, Philadelphia, 1998. Y. Saad. and M. H. Schultz. GMRES: A generalized minimal residual method for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7:856--869, 1986. http://www.stanford.edu/class/cme324/saad-schultz.pdf

Magnetometer construction and applications for introductory physics

Student-constructed magnetometers and commonly available software illustrate the use of autocorrelation functions to extract low-amplitude signals from background noise. The magnetometers are later used to measure forces at sampling rates over 50Hz, providing data for an introduction to numerical integration.

Computational model of modulation detection by the bullfrog

Bullfrog eighth-nerve fibers operate as envelope detectors, showing significant phase-locking to amplitude modulation (AM) rates as high as 800 Hz. A computational model that estimates stimulus period from all-order interval histograms (autocorrelation functions) aligned in time across frequency channels mimics fiber responses. The use of autocorrelation implies a mechanism based on delay lines or neural coincidence detection. The goal of this study was to determine the relevance of such a model in predicting responses of neurons in bullfrogs auditory midbrain (torus semicircularis) to AM stimuli. Modeled output of peripheral fibers was passed through a series of delay lines varying in latency, and then compared with actual midbrain data. There is a great diversity in representation of AM in the auditory midbrain, and this diversity is related to response latency and recording location. Neural responses from the cell sparse zone in the caudal midbrain were well-matched by a delay line mechanism, although the model was poorer in predicting response properties of other midbrain areas. [Work supported by NIH and the Brown University Brain Science Program.]

Homomorphism between cloudy and clear spectral radiance in the 800-900-cm(-1) atmospheric window region.

The sensitivity of a new algorithm for cloud detection over a sea surface has been assessed on the basis of extensive simulations of clear and cloudy radiance spectra, including water and ice and low- and high-altitude clouds. The new algorithm makes use of autocorrelation and cross correlation between an observed spectrum and either a synthetic or a laboratory spectrum and can be used to determine quantitatively the degree of homogeneity of two spectra in the 800-900-cm(-1) region (11.11-12.5 microm). The scheme is intended for high-spectral-resolution observations and could form the basis for an operational stand-alone cloud-detection algorithm for next-generation sounding spectrometers. Application of the scheme to real observations is presented and discussed.

Cloud detection over sea surface by use of autocorrelation functions of upwelling infrared spectra in the 800–900-cm^-1 window region

A new algorithm for cloud detection over sea surface has been developed that makes use of autocorrelation and cross correlation between a real spectrum and either a synthetic or a laboratory spectrum. The scheme is intended for high-spectral-resolution satelliteborne infrared sensors that will measure the Earth's entire emission spectrum rather than the upwelling radiance in a few channels. A new index is defined with which one can determine quantitatively the degree of homogeneity of two spectra in the 800-900-cm(-1) (11.11-12.5 mum) window region. The index makes use of only the observed spectrum along with a reference synthetic spectrum and, therefore, may form the basis for an operational stand-alone cloud-detection algorithm for next-generation high-spectral-resolution infrared sensors. Application both to synthetic spectra obtained in simulation and to sea-surface real spectra recorded through the interferometric monitor for greenhouse gases is considered.

Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode

We propose a novel self-mixing laser diode speckle velocimeter based on autocorrelation. The self-mixing laser diode launches and receives reflected light from a moving surface that has a random reflection profile. Some portion of the scattered light backcouples into the laser cavity and causes random intensity variations in the form of speckle signals. These speckle signals obtained from a self-mixing laser diode are processed by use of autocorrelation. The linear relation between the velocity and the reciprocal of the correlation time of the speckle intensity fluctuations allows us to determine the velocity easily if proper calibration is performed. The range of the investigated velocity is 20-450 mm/s. For an aluminum target that moves at a velocity of 350 mm/s, the measurement error is less than 2%.

High-accuracy wavelength-change measurement system based on a Wollaston interferometer, incorporating a self-referencing scheme

A novel wavelength-difference measurement scheme with a Wollaston prism is presented. By using a suitable reference wavelength, a small variation in the signal wavelength can be converted into a relatively larger change in the modulated wavelength, as a result of the so-called fringe beating effect, resulting in enhanced measurement sensitivity by use of autocorrelation and Gaussian filtering techniques. From the results of a simulation carried out, we observed a wavelength variation of 0.01 nm over 15 nm or 0.1 nm over 60 nm for a typical pair of laser diodes with wavelengths of 785 and 810 nm, and wavelength variations of 0.5 nm over 40 nm or 1 nm over 110 nm for 671-and 785-nm wavelengths. These results were partially verified by the experimental results obtained for which a resolution of 0.01 nm over a range of 2.5 nm for the first pair and 0.5 nm over 4 nm for the second pair of laser diodes was seen. The results have applications to the determination of wavelength variations in a wavelength-division multiplexing system or measurement of the wavelength changes induced in a range of optical sensors.

On the use of autocorrelation for pitch extraction: Some statistical considerations and their application to the sift algorithm

The aim of this paper is to consider the classical pitch determination method based on the short-time autorcorrelation analysis of the speech signal. Two commonly used estimators and the effect of signal windowing are taken into account. It is shown that in both periodic and purely random cases a similar decomposition holds for the estimated autocorrelation. Such a decomposition makes it possible to foresee the relative merits of the estimators considered, at least as far as gross pitch determination errors and voicing-errors are concerned. The expected behaviour is found to be in good agreement with results obtained through applying the SIFT algorithm to real speech.

On the use of autocorrelation in forecasting: Discussion of Aucamp and Eckardt's article in vol. 21, no. 1 of this journal

This note discusses a recent article concerned with various measures of autocorrelation and their appropriateness as tools for making forecasts. It aims to put the record straight on several points, and also suggests an improved way of looking at sample autocorrelations, when the purpose is to identify a plausible model from time series data.

Two caveats concerning the use of autocorrelations in forecasting

This article identifies two caveats regarding the calculation of autocorrelations when the approximate expression found in most forecasting software packages is employed. First, difficulties with the approximation are highlighted. A superior approximation is noted and discussed, although it is argued that the exact formula should be used. Second, it is suggested that the sample mean not be included in the computation of the autocorrelation function unless the null hypothesis of zero mean has been rejected. The Institute of Management Science, and the American Institute of Decision Sciences.

The Use of Auto-correlation for Pseudo-rank Determination in Noisy III-conditioned Linear Least-squares Problems

The determination of the pseudo-rank of a system of linear equations is complicated by ill-conditioning and the presence of noise in the matrix elements and/or data. A method is proposed for selecting a pseudo-rank suitable for calculating approximate least-squares solutions by considering auto-correlation properties of the residual vector. The method is inspired by one proposed by Powell for the fitting of curves to data, and presupposes a given ordering of the equations. The method is applied to selected ill-conditioned systems with added random noise, and the accuracy of the calculated solutions is investigated. Pseudo-ranks determined by generalized cross-validation are used for comparison, and the relative accuracy of the computed solutions is considered. Results indicate that auto-correlated pseudo-rank determination is a useful alternative to the method of generalized cross-validation, and that a combination of the two methods may yield more reliable selected pseudo-ranks.

Correlative firing patterns of serotonergic neurons in rat dorsal raphe nucleus

In this study, local neuronal interactions in the midbrain dorsal raphe nucleus (DRN) were analyzed by the use of autocorrelation and cross-correlation histograms. The autocorrelograms of serotonin (5-hydroxytryptamine; 5-HT)-containing cells showed an initial trough and subsequent periodicity which corresponded to their regular rhythmic firing pattern. Cross-correlograms revealed that all adjacent 5-HT neurons recorded from single micropipettes displayed complicated patterns of functional interactions. The interactions could be grouped into the following categories: (1) synchronization (interspike intervals less than 10 msec), (2) synchronization and direct inhibition, (3) synchronization and mutual inhibition. In contrast, cross-correlograms generated from adjacent neuronal pairs consisting of one 5-HT cell and one non-5-HT neuron or from non-adjacent 5-HT neuronal pairs usually failed to show functional interactions. The results of the present study are consistent with previous findings of a powerful auto-and mutual regulatory system for 5-HT neurons in the DRN.

Use of autocorrelation for the magnetic field in a cyclic accelerator designed to produce very high energies

Use of autocorrelation for the magnetic field in a cyclic accelerator designed to produce very high energies