a new approach to frequency analysis with amplified harmonics summary for stationary time series having a mixed spectrum we introduce a new method for estimating the discrete frequencies based on amplification of the sine waves in the time series and on minimization of least squares regressions on amplified waves under the assumption that the continuous part of the spectrum arises from a stationary autoregressive moving average process we show that the estimators for the discrete frequencies obtained with this method are strongly consistent more precisely as the serial length n tends to infinity their bias almost surely converges to zero with the rate n 3 2 log n 5 6 2 we also establish a central limit theorem which shows that these estimators have exactly the same asymptotic variance as that given by whittle s method which is known to yield the most accurate frequency estimates however the new technique has two advantages over whittle s method first it yields an algorithm that is both robust against improper starting estimates and computationally efficient secondly it gives rise to a simple tool based on its amplified harmonics for identifying the number of sine waves in a time series a simulation study is also reported that gives statistical results on the properties of the new method on simulated series as well as comparative results with whittle s method

performance analysis of an adaptive notch filter with constrained poles and zeros a statistical analysis of the sine wave frequency estimate obtained by the adaptive notch filter anf recently proposed by a nehorai ibid vol assp 33 p 983 96 aug 1985 is presented asymptotically valid expressions for the bias and mean square error of the frequency estimate are provided the analysis verifies the performance exhibited by the anf and clarifies the role of some user variables such as the notch bandwidth and the number of data samples processed

the weight distributions of the duals of cyclic codes with two zeros cyclic codes with two zeros and their dual codes have been a subject of study for many years however their weight distributions are known only for a few cases in this paper the weight distributions of the duals of the cyclic codes with two zeros are settled for a few more cases

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

cyclic codes and sequences from generalized coulter matthews function in this paper we will study the exponential sum sigmaxisinfq x alphax pk 1 2 betax that is related to the generalized coulter matthews function x pk 1 2 with k gcd as applications we obtain the following the correlation distribution of a p ary m sequence and a decimated m sequence of degree pk 1 2 the weight distribution of the cyclic code whose dual has two zeros pi 1 and pi pk 1 2

estimating the number of sinusoids in additive white noise the test proposed uses the eigenvector decomposition of the estimated autocorrelation matrix and is based on matrix perturbation analysis the estimator is shown to be able to resolve closely spaced sinusoids at lower signal to noise ratios than heuristic tests simulation results for two closely spaced sinusoids are detailed several unanswered questions are discussed

linear prediction approach for efficient frequency estimation of multiple real sinusoids algorithms and analyses based on the linear prediction property of sinusoidal signals two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed in order to achieve accurate frequency estimation the first algorithm uses a generalized unit norm constraint while the second method employs a monic constraint the weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner for the case of a single real tone with sufficiently large data samples both estimators provide nearly identical frequency estimates and their performance approaches crame spl acute r rao lower bound crlb for white gaussian noise before the threshold effect occurs algorithms for closed form single tone frequency estimation are also devised computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the crlb for different frequencies observation lengths and signal to noise ratio snr conditions

the box crossing property for critical two dimensional oriented percolation we consider critical oriented bernoulli percolation on the square lattice mathbb z 2 we prove a russo seymour welsh type result which allows us to derive several new results concerning the critical behavior the sub linear polynomial fluctuations contrast with the supercritical regime where w n is known to behave linearly in n it is also different from the critical picture obtained for non oriented bernoulli percolation in which the scaling limit is non degenerate in both directions all our results extend to the graphical representation of the one dimensional contact process

zero crossing rates of mixtures and products of gaussian processes formulas for the expected zero crossing rate of non gaussian mixtures and products of gaussian processes are obtained the approach we take is to first derive the expected zero crossing rate in discrete time and then obtain the rate in continuous time by an appropriate limiting argument the processes considered which are non gaussian but derived from gaussian processes serve to illustrate the variability of the zero crossing rate in terms of the normalized autocorrelation function p t of the process for gaussian processes rice s formula gives the expected zero crossing rate in continuous time as 1 spl pi spl radic spl rho 0 we show processes exist with expected zero crossing rates given by spl kappa spl pi spl radic spl rho 0 with either spl kappa spl gt 1 or spl kappa spl lt 1 consequently such processes can have an arbitrarily large or small zero crossing rate as compared to a gaussian process with the same autocorrelation function

the weight enumerator of three families of cyclic codes cyclic codes are a subclass of linear codes and have wide applications in consumer electronics data storage systems and communication systems due to their efficient encoding and decoding algorithms cyclic codes with many zeros and their dual codes have been a subject of study for many years however their weight distributions are known only for a very small number of cases in general the calculation of the weight distribution of cyclic codes is heavily based on the evaluation of some exponential sums over finite fields very recently li studied a class of p ary cyclic codes of length p2m 1 where p is a prime and m is odd they determined the weight distribution of this class of cyclic codes by establishing a connection between the involved exponential sums with the spectrum of hermitian forms graphs in this paper this class of p ary cyclic codes is generalized and the weight distribution of the generalized cyclic codes is settled for both even m and odd m along with the idea of li the weight distributions of two related families of cyclic codes are also determined

a generalized least squares method for frequency estimation the application of the generalized least squares gls method to the estimation of the frequencies of sinusoids in additive colored noise is discussed an iterative algorithm is proposed starting from the assumption that the parameter vector in the model of the sinusoids is symmetric the algorithm utilizes an adaptive strategy for contracting the poles of the estimated signal model expressions for the probability limit and the asymptotic variance of the estimates are derived for the single sinusoid case possible convergence points and the asymptotic behavior of the algorithm in the case of low snrs signal to noise ratios are analyzed extensive simulation results show that the algorithm represents a simple and reliable tool for practical applications

model parameter estimation for reciprocal gaussian random processes the problem of estimating the model parameters of a discrete index reciprocal gaussian random process from a limited number of noisy observations is addressed the general case of a first order multivariate process is analyzed stating its basic properties and deriving a linear equation set that relates the model parameters including the unknown variance of the observation noise to the generally nonstationary autocorrelation function of the observed process it generalizes to the reciprocal processes the so called high order yule walker equations for ar processes based on these results a practical estimation algorithm is proposed

spectral zero crossings localization properties and applications we present an analysis of the rate of sign changes in the discrete fourier spectrum of a sequence the sign changes of either the real or imaginary parts of the spectrum are considered and the rate of sign changes is termed as the spectral zero crossing rate szcr we show that szcr carries information pertaining to the locations of transients within the temporal observation window we show duality with temporal zero crossing rate analysis by expressing the spectrum of a signal as a sum of sinusoids with random phases this extension leads to spectral domain iterative filtering approaches to stabilize the spectral zero crossing rate and to improve upon the location estimates the localization properties are compared with group delay based localization metrics in a stylized signal setting well known in speech processing literature we show applications to epoch estimation in voiced speech signals using the szcr on the integrated linear prediction residue the performance of the szcr based epoch localization technique is competitive with the state of the art epoch estimation techniques that are based on average pitch period

weight distributions of some binary primitive cyclic codes let s and k be integers such that s is a divisor of 2 sup k 1 let g x be a divisor of x sup s 1 over f sub 2 and let spl pi x be a primitive polynomial of degree k over f sub 2 we consider the binary cyclic code c of length n 2 sup k 1 generated by x sup n 1 g x spl pi x for special cases we determine the weight distribution of c by using the weights of the cyclic code of length s generated by x sup s 1 g x

asymptotic behavior of maximum likelihood estimates of superimposed exponential signals strong consistency and asymptotic normality are derived for the maximum likelihood estimates mles of the unknown parameters omega sub 1 omega sub p alpha sub 1 alpha sub p and sigma sup 2 in the superimposed exponential model for signals y sub t sigma alpha exp it omega sub k e sub t where the summation is from k 1 to p t 0 1 n 1 and sigma sup 2 is the variance of the complex normal distribution of e sub t as a by product it is found that the mles of the parameters attain the cramer rao lower bound for the asymptotic covariance matrix

a family of five weight cyclic codes and their weight enumerators cyclic codes are a subclass of linear codes and have applications in consumer electronics data storage systems and communication systems as they have efficient encoding and decoding algorithms in this paper a family of p ary cyclic codes whose duals have three pairwise nonconjugate zeros is proposed the weight distribution of this family of cyclic codes is determined it turns out that the proposed cyclic codes have five nonzero weights

the weight enumerator of a class of cyclic codes cyclic codes with two zeros and their dual codes have been a subject of study for many years however their weight distributions are known only for a few cases in this paper the weight distributions of the duals of the cyclic codes with two zeros are settled for a few cases the weight distributions of punctured versions of these codes are also determined for several special cases

narrowband acoustic doppler volume backscattering signal ii spectral centroid estimation for pt i see ibid vol 50 p 2644 2655 2002 this paper proposes a novel algorithm to estimate the time varying spectral centroid of the narrowband doppler volume backscattering signal it is constructed in a semi parametric way that is modeling parametrically the local narrowband evolutionary spectrum using an ar 2 and nonparametrically adapting its time varying coefficients using the wavelet shrinkage the improved performance is gained by the underlying linear prediction function of the ar 2 and the minimax optimality of the unknown smoothness adaptation of the wavelet shrinkage procedure

gradient based adaptive iir notch filtering for frequency estimation the use of gradient based algorithms with infinite impulse response iir notch filtering for estimating sinusoids imbedded in noise is investigated two notch filter model structures are presented the first is for applications where two signal sources with correlated noise components can be assessed the second can be used in situations where only one composite signal source is available error surface analysis indicates that second order modules are unimodal and result in guaranteed convergence higher order modules are multimodal and require judicious choice of initial parameter estimates simulation results are included to demonstrate the performance characteristics of both filter structures

on frequency estimation summary t this paper discusses a least squares procedure and the use of the periodogram for isolating a discrete harmonic of a time series it is shown that the usual asymptotics on estimation of frequency amplitude and phase of such a harmonic have to be used with great caution from a moderate sample perspective computational issues are discussed and some illustrations are provided bolt brillinger 1979 make use of these asymptotic results we consider a time series model of the form x a cos wt f e where e is a stationary noise sequence and one is interested in estimating the amplitude frequency and phase of the harmonic component the asymptotic theory of the least squares estimates of these parameters has a long history whittle 1951 1953 obtained some of the earliest results more recent results are by hasan 1982 hannan 1973 and walker 1971 who formalize and extend whittle s results in these works it is shown that the asymptotic variance of the frequency estimate is of order n 3 and that the asymptotic variances of the other two components are of the more usual order n these results extend when there are several harmonic components the rate for the estimate of w seems almost unbelievably good and our work was motivated by a desire to see how reliable the asymptotic theory is in brief we find that the product of the amplitude and the sample size n must be quite large in order for the asymptotic theory to be meaningful if this product is not large the frequency estimate is much more variable than indicated by the asymptotic theory and the amplitude estimate is severely biased in applications in which the amplitude is small giving rise to a small peak in the periodogram these results suggest that naive application of the asymptotic theory to gauge resolution can be quite misleading section 2 of this paper is devoted to a review and examination of the asymptotic theory we are also concerned with computational issues arising from the least squares problem this problem is nonlinear in the parameters so that some sort of iterative search must be employed typically search methods start from an initial guess and then proceed by a sequence of modified newton raphson steps for this nonlinear least squares problem it turns out that there are many local minima with a separation in frequency about n l which makes the stationary point to which the iterative scheme converges extremely sensitive to the starting values and this problem gets worse as the sample size increases furthermore it follows from the results of 2 that the estimate of the amplitude is very biased unless the frequency is resolved with order o n so that failure to converge to the global minimum may give a very poor estimate of amplitude the problem becomes

higher order crossings spectral analysis of an almost periodic random sequence in noise the precise effect of noise on hoc higher order crossing sequences is examined settling some issues not dealt with previously it is shown that it is possible to construct hoc sequences that converge to true discrete frequencies in a mixed spectrum even for very low signal to noise ratios the availability of the correlation function is then assumed when the expected hocs from repeated differences are known the correlation function is automatically known as well however other quantities not just the expected hoc can serve the same purpose for example under the gaussian assumption the correlation function can be obtained from that of the binary process derived by clipping the original process at any level

asymptotic analysis of a fast algorithm for efficient multiple frequency estimation based on an asymptotic analysis of the contraction mapping cm method of li and kedem 1993 a bandwidth shrinkage rule is proposed for fast and accurate estimation of the frequencies of multiple sinusoids from noisy measurements the cm frequency estimates are defined as the fixed points of a contractive mapping formed by the lag one autocorrelation coefficient calculated from the output of a parametric filter applied to the observed time series with bandwidth parameters judiciously chosen according to the asymptotic analysis the algorithm is shown to be able to accommodate possibly poor initial values of precision o n sup 1 3 and converge to a final estimate whose accuracy is arbitrarily close to o n sup 3 2 the optimal error rate for frequency estimation under the gaussian assumption the total computational complexity of the algorithm is shown to be o n log n which is comparable to that of n point fast fourier transform fft a novelty in the asymptotic analysis is that it accommodates closely spaced frequencies by allowing not only the filter bandwidth but also the frequency separation to be functions of the sample size n this enables an assessment of the accuracy of the frequency estimates for given bandwidths and initial values in situations where some or all of the frequencies are close to each other

the weight distribution of a class of cyclic codes related to hermitian forms graphs the determination of weight distribution of cyclic codes involves the evaluation of gauss sums and exponential sums despite some cases where a neat expression is available the computation is generally rather complicated in this note we determine the weight distribution of a class of reducible cyclic codes whose dual codes may have arbitrarily many zeros this goal is achieved by building an unexpected connection between the corresponding exponential sums and the spectra of hermitian forms graphs

optimal cyclic codes with generalized niho type zeros and the weight distribution in this paper we extend two earlier works further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions it is interesting to note that many cyclic codes in the family are optimal and have only a few non zero weights besides using similar ideas we carry out some subtle manipulation of certain exponential sums

a fast efficient technique for the estimation of frequency summary a technique is presented for the estimation of the frequency of a sinusoid in the presence of noise the technique is based on fitting arma 2 2 models iteratively in a special way the estimator is shown to be strongly consistent and as efficient as the least squares estimator of the frequency or the periodogram maximizer a simple accelerated version of the technique is shown to converge in a small number of iterations the number depending on the accuracy of the initiator of the procedure the results of a number of simulations are reported

frequency domain prony method for autoregressive model identification and sinusoidal parameter estimation in this study the weighted integral method for identifying differential equation models is extended to a discrete time system with a difference equation de model and a finite length sampled data sequence and obtain a frequency domain algorithm for short time signal analysis and frequency estimation the derivation consists of three steps 1 provide the de autoregressive model with unknown coefficients which is satisfied in a finite observation interval 2 discrete fourier transform dft the de to obtain algebraic equations aes among the fourier coefficients two mathematical techniques are introduced to maintain the circulant nature of time shifts 3 simultaneously solve a sufficient number of aes with least squares criterion to obtain unknowns exactly when the driving term is absent or to obtain unknowns that minimize the driving power when it is present the methods developed enable a decomposed processing of identification and estimation in the frequency domain thus they will be suitable for maximizing statistical efficiency smallness of estimation error variance reducing the computational cost and use in a resolution enhanced time frequency analysis of real world signals the performance of the proposed methods are compared with those of several dft based methods and cramer rao lower bound also the interference effect and its reduction in frequency decomposed processing are examined

iterative filtering for multiple frequency estimation it is well known that prony s least squares estimator gives inconsistent estimates for multiple frequency estimation in a recent attempt to diminish this problem dragosevic and stankovic 1989 couple the least squares method of autoregressive ar estimation with an iterative filtering scheme discussed by kay 1988 using an all pole filter but the inconsistency still persists this paper attacks the chronic inconsistency with a general approach of parametric filtering that unifies and extends the previous work it is shown that the inconsistency can be eliminated with an appropriately parametrized filter the clue for the correct parametrization comes from a formula for the bias of the least squares ar estimator the fact of the matter is that as long as a filter satisfies the parametrization requirement consistent estimates can be obtained from the least squares ar estimator on the basis of the filtered data in particular the all pole filter considered by dragosevic and stankovic can be easily reparametrized so that it too satisfies the parametrization requirement and thus leads to a consistent estimator experimental results show that the modified method has a higher resolution than the discrete fourier transform and that its overall performance is quite remarkable

the central limit theorem for the right edge of supercritical oriented percolation on demontre un theoreme central limite pour la croissance des bords droits d une percolation orientee supercritique la technique de demonstration utilisee est de trouver des points avec des proprietes d un type de regeneration appeles points de ruptures cette technique peut etre appliquee a d autres processus

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

on convergence and bias correction of a joint estimation algorithm for multiple sinusoidal frequencies twenty years ago kay proposed an iterative filtering algorithm ifa for jointly estimating the frequencies of multiple complex sinusoids from noisy observations ifa is based on the fact that the noiseless signal is an autoregressive ar process so the frequency estimation problem can be reformulated as the problem of estimating the ar coefficients by iterating the cycle of ar coefficient estimation and ar filtering ifa provides a computationally simple procedure yet capable of accurate frequency estimation especially at low signal to noise ratio snr however the convergence of ifa has not been established beyond simulation and a very special case of a single frequency and infinite sample size this article provides a statistical analysis of the algorithm and makes several important contributions it shows that the poles of the ar filter must be reduced by an extra shrinkage parameter to accommodate poor initial values and avoid being trapped into false solutions it also shows that the ar estima

some contributions to a frequency location method due to he and kedem the author derives a useful information theoretical technology from the tunable filter that automatically detects the frequency of an unknown signal in white gaussian noise by adjusting its parameter to the correlation coefficient of its output the tunable filter earlier proposed by s he and b kedem see ibid vol 35 no 2 p 360 9 1989 is known as the hk filter the methodology sidesteps the white noise and normality assumptions more importantly it is shown that broad classes of linear filters can be made to implement the detection plan in particular bandpass filters can be expected to lock in even more quickly and accurately than the hk filter this analysis yields a formula for the error contraction at each recursion

zero crossing statistics for non markovian time series in applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time to failure of fatigued materials researchers and engineers want to calculate how often a stochastic observable crosses a specific level such as zero at first glance this problem looks simple but it is in fact theoretically very challenging and therefore few exact results exist one exception is the celebrated rice formula that gives the mean number of zero crossings in a fixed time interval of a zero mean gaussian stationary process in this study we use the so called independent interval approximation to go beyond rice s result and derive analytic expressions for all higher order zero crossing cumulants and moments our results agree well with simulations for the non markovian autoregressive model

an exact direct method of sinusoidal parameter estimation derived from finite fourier integral of differential equation in this paper we propose a novel method for estimating the parameters frequency amplitude and phase of real sinusoids to derive the estimator we start from the characteristic differential equation of a sinusoid to remove differentials and obtain an algebraic relation for frequency we introduce finite period weighted integrals of the differential equation which become equivalent to the differential equation when a sufficient number of weight functions are applied as weight functions we show that fourier kernels have excellent properties terms related to integral boundaries are readily eliminated observations are provided by fourier coefficients and the relation becomes independently accurate for multiple sinusoids if they are sufficiently spaced we solve the obtained equations in two ways one is for approaching to the cramer rao lower bound crlb and the other is for enhancing the interference rejection capability also methods are proposed to calculate the weighted integrals from sampled signals with an improved accuracy proposed algorithms are examined under noise and sinusoidal interference error variances are compared with the crlb and other fast fourier transform fft based methods

the contact process on a finite set ii in this paper we complete the work started in part i we show that if sigma n is the time that the contact process on 1 ldots n first hits the empty set then for lambda lambda c the critical value for the process on z there is a positive constant gamma lambda so that log sigma n n rightarrow gamma lambda in probability as n rightarrow infty we also give a new simple proof that sigma n e sigma n converges to a mean one exponential the keys to the proof of the first result are a planar graph duality for the contact process and an observation of j chayes and l chayes that exponential decay rates for connections in strips approach the decay rates in the plane as the width of the strip goes to infty

estimation of the parameters of sinusoidal signals in non gaussian noise accurate estimation of the amplitude and frequency parameters of sinusoidal signals from noisy observations is an important problem in many signal processing applications in this paper the problem is investigated under the assumption of non gaussian noise in general and laplace noise in particular it is proven mathematically that the maximum likelihood estimator derived under the condition of laplace white noise is able to attain an asymptotic cramer rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares it is also proven that when applied to non laplace situations the laplace maximum likelihood estimator which may also be referred to as the nonlinear least absolute deviations estimator can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails a computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function simulation results are provided to validate the analytical findings

cyclic codes and sequences the generalized kasami case in this paper the large family of generalized kasami sequences has been studied in particular the cross correlation distribution among these sequences has been explicitly calculated meanwhile the weight distributions of two classes of cyclic codes could also be determined this paper generalizes the results from several previous papers

hamming weights of the duals of cyclic codes with two zeros cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms in this paper let bbb f r be a finite field with r q m suppose that g 1 g 2 in bbb f r are not conjugates over bbb f q operatorname ord g 1 n 1 operatorname ord g 2 n 2 d gcd n 1 n 2 and n n 1n 2 d let bbb f q g 1 bbb f q m 1 bbb f q g 2 bbb f q m 2 and text t i denote the trace function from bbb f q m i to bbb f q for i 1 2 we define a cyclic code mathcal c q m n 1 n 2 c a b a in bbb f q m 1 b in bbb f q m 2 where c a b text t 1 ag 1 0 text t 2 bg 2 0 text t 1 ag 1 1 text t 2 bg 2 1 ldots text t 1 ag 1 n 1 text t 2 bg 2 n 1 we mainly use gauss periods to present the weight distribution of the cyclic code mathcal c q m n 1 n 2 as applications we determine the weight distribution of cyclic code mathcal c q m q m 1 1 q m 2 1 with gcd m 1 m 2 1 in particular it is a three weight cyclic code if gcd q 1 m 1 m 2 1 we also explicitly determine the weight distributions of some classes of cyclic codes including several classes of four weight cyclic codes

the contact process on a finite set iii the critical case we show that in n is the time that the contact process on 1 n first hits the empty set then for c the critical value for the contact process on z n n and n n 4 0 in probability as n as a consequence of the result we get bounds on some critical exponents we also study the analogous problem for bond percolation in 1 n z and investigate the limit distribution of n e n

autoregressive frequency estimation summary presume that an autoregressive model of given order is fitted to data obtained from a realization of a sinusoidal signal embedded in white noise this paper investigates the statistical properties of the estimate of the frequency of the signal obtained by minimizing the transfer function of the autoregression strong consistency and convergence in distribution of the estimate are established when the order of the autoregression is allowed to increase with sample size at an appropriate rate it is also shown that the operational characteristics of commonly used order determination procedures are such as to produce values of the selected order compatible with the application of the asymptotic theory the outcome of some simulation experiments and an empirical example illustrating the practical impact of the results obtained are also presented

edge fluctuations for the one dimensional supercritical contact process we consider the one dimensional supercritical contact process with initial configurations having infinitely many particles to the left of the origin and only finitely many to its right starting from any such configuration we first prove that in the limit as time goes to infinity the law of the process as seen from the edge converges to the invariant distribution constructed by durrett 12 we then prove a functional central limit theorem for the fluctuations of the edge around its average showing that the corresponding diffusion coefficient is strictly positive we finally characterize the space time structure of the system in particular we prove that its distribution shifted in space by at t denotes the time and a the drift of the edge converges when t goes to infinity to a 2 2 mixture of the two extremal invariant measures for the contact process 1 introduction in this article we study the one dimensional supercritical contact process a stochastic process with infinitely many interacting particles which move on z the set of all the integers we consider initial states with infinitely many particles to the left of the origin and finitely many to its right we first prove that at large times the state of the system approaches some definite structure which as time increases rigidly shifts to the right a steady state propagates from the left to the right with constant speed through the formerly empty region the system is a very schematic and rough microscopic model for the formation and propagation of one dimensional shock waves as we shall see in some more detail in the sequel at large times we can distinguish three different space regions the first two are semiinfinite intervals which extend to oo and oo respectively while the third one is the interval which connects the first two in the first region the state looks like the nonzero density equilibrium state for the supercritical contact process while in the second it is the empty state the third is the interesting region it describes the wave front we find that the state there is close to a superposition of the two extremal equilibrium states the weight of the decomposition ranges from 1 all the weight to the nonzero density state to 0 as one moves from left to right as the time t increases the previous picture shifts to the right and at the same time the size of the front wave increases like tl 2 the picture is very similar indeed to that found by wick 25 in a zero range model our result is a consequence of a very detailed analysis of the motion of the first particle in the system the edge and of a precise knowledge of the structure of the state as seen from the edge such

strong consistency of the contraction mapping method for frequency estimation some statistical properties in regard to the contraction mapping cm method are discussed one of the requirements in this method is that the filter be parameterized to satisfy a certain fundamental property the parameterization clearly depends on the normalized noise spectrum which theoretically has to be known or estimated a priori if this information is available one can first whiten the noise with a linear filter and then apply the cm method to the filtered data in this way the parameterization only needs to be done under the white noise assumption and filters like the ar 2 can be used by the cm method in applications however prewhitening may not always be necessary

improved lower bounds for the critical probability of oriented bond percolation in two dimensions we present a coupled decreasing sequence of random walks on z that dominate the edge process of oriented bond percolation in two dimensions using the concept of random walk in a strip we describe an algorithm that generates an increasing sequence of lower bounds that converges to the critical probability of oriented percolation pc from the 7th term on these lower bounds improve upon 0 6298 the best rigorous lower bound at present establishing 0 63328 as a rigorous lower bound for pc finally a monte carlo simulation technique is presented the use thereof establishes 0 64450 as a non rigorous five digit precision lower estimate for pc

weight distributions of two classes of cyclic codes with respect to two distinct order elements cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms cyclic codes have been studied for many years but their weight distributions are known only for a few cases in this paper let fr be an extension of a finite field fq and r qm we determine the weight distributions of the cyclic codes c c a b a b fr c a b trr q ag10 bg20 trr q ag1n 1 bg2n 1 g1 g2 fr in the following two cases 1 ord g1 n n r 1 and g2 1 and 2 ord g1 n g2 g12 ord g2 n 2 m 2 and 2 r 1 n q 1

the critical contact process dies out by producing a finite box criterion for survival in a slab we show that the critical contact process dies out and that in two and more dimensions the critical parameter value coincides with the limit of slab thresholds using the techniques developed in this paper one may obtain the complete convergence and shape theorems for contact processes in all dimensions and for all infection rates our results apply also to the discrete time analogue of the contact process viz oriented percolation

scaling inequalities for oriented percolation we look at seven critical exponents associated with two dimensional oriented percolation scaling theory implies that these quantities satisfy four equalities we prove five related inequalitites

correlation lengths for oriented percolation oriented percolation has two correlation lengths one in the space and one in the time direction in this paper we define these quantities for the two dimensional model in terms of the exponential decay of suitably chosen quantities and study the relationship between the various definitions the definitions are used in a companion paper to prove inequalities between critical exponents

on the weight distributions of two classes of cyclic codes let q pm where p is an odd prime mges2 and 1lesklesm 1 let tr be the trace mapping from fq to fp and zetap e2pii p be a primitive pth root of unity in this paper we determine the value distribution of the following exponential sums sigmaxisinf qchi alphaxp k 1 betax2 alpha betaisinfq where chi x zetap tr x is the canonical additive character of fq as applications we have the following 1 we determine the weight distribution of the cyclic codes c1 and c2 over fpt with parity check polynomial h2 x h3 x and h1 x h2 x h3 x respectively where t is a divisor of d gcd m k and h1 x h2 x and h3 x are the minimal polynomials of pi 1 pi 2 and pi p k 1 over fpt respectively for a primitive element pi of fq 2 we determine the correlation distribution between two m sequences of period q 1 moreover we find a new class of p ary bent functions this paper extends the results in feng and luo 2008