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autocorrelation Function of a Family of Complex Sequences

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Chinese Science Bulletin 1994年第11期39卷 881-885页

作者：李超 National University of Defence Technology Changsha 410003 PRC

In 1984, R. A. Scholtz and L. R. Welch constructed a series of new binary se-quences which are called GMW sequences by using the trace function as follows: LetM, J be positive integers, J|M, α be a primitive element of the finite field GF（2M）, rbe a positive integer, 1≤r≤2J, and（r, 2J-1）=1. Then the sequence b=b（0）b（1）…b（n）…is called GMW sequence over GF（2）. Here b（n）=tr1J（trJMαn）r, for n=0, 1, 2….

关键词： finite field trace function autocorrelation function.

Complete characterization of ultrafast optical fields by phase-preserving nonlinear autocorrelation

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Light(Science & Applications) 2022年第10期11卷 2451-2462页

作者： Alexander Gliserin Soo Hoon Chew Seungchul Kim Dong Eon Kim Department of Optics and Mechatronics Engineering College of Nanoscience and NanotechnologyPusan National University2 Busandaehak-ro 63beon-gilBusan 46241South Korea Department of Cogno Mechatronics Engineering College of Nanoscience and NanotechnologyPusan National University2 Busandaehak-ro 63beon-gilBusan 46241South Korea Max Planck Center for Attosecond Science Max Planck POSTECH/Korea Research Initiative77 Cheongam-roPohang 37673South Korea Department of Physics Center for Attosecond Science and TechnologyPohang University of Science and Technology77 Cheongam-roPohang 37673South Korea

Nonlinear autocorrelation was one of the earliest and simplest tools for obtaining partial temporal information about an ultrashort optical pulse by gating it with ***,since the spectral phase is lost in a conventional autocorrelation measurement,it is insufficient for a full characterization of an ultrafast electric field,requiring additional spectral information for phase ***,we show that introducing an intensity asymmetry into a conventional nonlinear interferometric autocorrelation preserves some spectral phase information within the autocorrelation signal,which enables the full reconstruction of the original electric field,including the direction of time,using only a spectrally integrating *** call this technique Phase-Enabled Nonlinear Gating with Unbalanced Intensity(PENGUIN).It can be applied to almost any existing nonlinear interferometric autocorrelator,making it capable of complete optical field characterization and thus providing an inexpensive and less complex alternative to methods relying on spectral measurements,such as frequency-resolved optical gating(FROG)or spectral phase interferometry for direct electric-field reconstruction(SPIDER).More importantly,PENGUIN allows the precise characterization of ultrafast fields in non-radiative(e.g.,plasmonic)nonlinear optical interactions where spectral information is *** demonstrate this novel technique through simulations and experimentally by measuring the electric field of~6-fs laser pulses from a Ti:sapphire *** results are validated by comparison with the well-established FROG method.

关键词： autocorrelation nonlinear characterization

Linear complexity and autocorrelation of a new class of binary generalized cyclotomic sequences of order two and length pqr

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Journal of Systems Engineering and Electronics 2019年第4期30卷 651-661页

作者： JIA Wenjuan GAO Juntao ZHANG Peng School of Telecommunications Engineering Xidian UniversityXi’an 710071China The State Key Laboratory of Integrated Services Network Xidian UniversityXi’an 710071China

Cyclotomic sequences have good cryptographic properties and are closely related to difference *** paper proposes a new class of binary generalized cyclotomic sequences of order two and length *** linear complexity,minimal polynomial,and autocorrelation are *** results show that these sequences have a large linear complexity when 2∈D1,which means they can resist the Berlekamp-Massey ***,the autocorrelation values are close to 0 with a probability of approximately 1?1/***,when r is a big prime,the new sequence has a good autocorrelation.

关键词： generalized cyclotomic sequence linear complexity minimal polynomial autocorrelation value.

An Improved Markov Chain Model Based on autocorrelation and Entropy Techniques and Its Application to State Prediction of Water Resources

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Chinese Geographical Science 2011年第2期21卷 176-184页

作者： ZHOU Ping ZHOU Yuliang JIN Juliang LIU Li WANG Zongzhi CHENG Liang ZHANG Libing College of Hydrology and Water Resources Hohai University Nanjing 210098 China College of Civil Engineering Hefei University of Technology Hefei 230009 China State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Nanjing Hydraulic Research Institute Nanjing 210029 China

According to the relationships among state transition probability matrixes with different step lengths, an improved Markov chain model based on autocorrelation and entropy techniques was introduced. In the improved Markov chain model, the state transition probability matrixes can be adjusted. The steps of the historical state of the event, which was significantly related to the future state of the event, were determined by the autocorrelation technique, and the impact weights of the event historical state on the event future state were determined by the entropy technique. The presented model was applied to predicting annual precipitation and annual runoff states, showing that the improved model is of higher precision than those existing Markov chain models, and the determination of the state transition probability matrixes and the weights is more reasonable. The physical concepts of the improved model are distinct, and its computation process is simple and direct, thus, the presented model is sufficiently general to be applicable to the prediction problems in hydrology and water resources.

关键词： improved Markov chain model autocorrelation entropy annual precipitation annual runoff genetic algorithm

Confocal laser speckle autocorrelation imaging of dynamic flow in microvasculature

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Opto-Electronic Advances 2022年第2期5卷 22-32页

作者： E Du Shuhao Shen Anqi Qiu Nanguang Chen Department of Biomedical Engineering National University of Singapore7 Engineering Drive 1Singapore 117574Singapore

Laser speckle imaging has been widely used for in-vivo visualization of blood perfusion in biological ***,existing laser speckle imaging techniques suffer from limited quantification accuracy and spatial *** we re-port a novel design and implementation of a powerful laser speckle imaging platform to solve the two critical *** core technique of our platform is a combination of line scan confocal microscopy with laser speckle autocorrelation imaging,which is termed Line Scan Laser Speckle autocorrelation Imaging(LS-LSAI).The technical advantages of LS-LSAI include high spatial resolution(~4.4μm)for visualizing and quantifying blood flow in microvessels,as well as video-rate imaging speed for tracing dynamic flow.

关键词： laser speckle autocorrelation confocal line scan flow

Heteroscedasticity and/or autocorrelation Checks in Longitudinal Nonlinear Models with Elliptical and AR(1) Errors

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Acta Mathematicae Applicatae Sinica 2012年第1期28卷 49-62页

作者： Chun-Zheng CAO Jin-Guan LIN College of Math&Physics Nanjing University of Information Science&TechnologyNanjing 210044China Department of Mathematics Southeast UniversityNanjing 210096China

The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR（1） errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-S, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-squave and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.

关键词： autocorrelation elliptical distributions heteroscedasticity longitudinal data nonlinear model,score test

Assessment and improvement of autocorrelation performance of chaotic sequences using a phase space method

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Science China(Information Sciences) 2011年第12期54卷 2667-2679页

作者： CHEN Bin School of Software and Communication Engineering, JiangXi University of Finance and Economy, Nanchang 330032, China School of Software and Communication Engineering JiangXi University of Finance and Economy Nanchang China

Chaotic sequences have been widely used as pseudorandom sequences. However, how to judge whether their autocorrelation performance is good remains a problem because we have no simple method for assessing and improving the autocorrelation performance. Using a phase space method, we have discovered that the autocorrelation performance of a chaotic sequence is determined by whether its phase space trajectory is axis symmetrical, and have deduced theorems to describe and solve these problems. This paper presents a simple yet effective method to assess and improve the autocorrelation performance of chaotic sequences. Several simulations are presented to validate the theorems and method.

关键词： chaos autocorrelation pseudorandom sequences phase space

Test for autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Lévy processes

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Science China Mathematics 2013年第2期56卷 339-357页

作者： ZHANG ShiBin ZHANG XinSheng Department of Mathematics Shanghai Maritime University Department of Statistics Fudan University

In this paper, we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Levy processes. For a test, we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations. It is shown that each of the test statistics weakly converges to the supremum of the square of a Brownian bridge. The test statistics are evaluated by some empirical results.

关键词： autocorrelation Brownian bridge cusum test Ornstein-Uhlenbeck test for parameter change,weak convergence

Photoacoustic Doppler flowmetry of carbon particles flow using an autocorrelation method

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Optoelectronics Letters 2014年第6期10卷 467-469页

作者：卢涛 College of Electrical Engineering Henan University of Technology

In order to measure the axial flowing velocity of carbon particle suspension with particle diameter of tens of micrometers, the photoacoustic Doppler(PAD) frequency shift is calculated based on a series of individual A scans using an autocorrelation method. A 532 nm pulsed laser with repetition rate of 20 Hz is used as a pumping source to generate photoacoustic signal. The photoacoustic signals are detected using a focused piezoelectric(PZT) ultrasound transducer with central frequency of 5 MHz. The suspension of carbon particles is driven by a syringe pump. The complex photoacoustic signal is calculated by the Hilbert transformation from time-domain photoacoustic signal, and then it is autocorrelated to calculate the Doppler frequency shift. The photoacoustic Doppler frequency shift is calculated by averaging the autocorrelation results of some individual A scans. The advantage of the autocorrelation method is that the time delay in autocorrelation can be defined by user, and the requirement of high pulse repetition rate is avoided. The feasibility of the proposed autocorrelation method is preliminarily demonstrated by quantifying the motion of a carbon particle suspension with flow velocity from 5 mm/s to 60 mm/s. The experimental results show that there is an approximately linear relation between the autocorrelation result and the setting velocity.

关键词： autocorrelation Carbon Doppler effect Flow velocity Frequency shift keying Mathematical transformations Optical pumping Pulse repetition rate Time delay Time domain analysis Ultrasonic transducers