two dimensional period estimation by ramanujan s sum period estimation in one dimension 1 d has been studied for years however 2 d period estimation is still a hard problem since it has three parameters to determine length width and direction recently a special kind of 2 d function called 2d gcd delta function is proposed it has close relationship with ramanujan s sum and the 2 d periodicity matrix in this paper we will describe how to use this function to decompose an image into subband signals each subband signal will have its own periodicity matrix so we also provide a simple algorithm to calculate the least common multiple lcm of those subband signal periodicity matrices concrete experiments are given to prove the robustness of the proposed 2 d period estimation method

approximate maximum likelihood period estimation from sparse noisy timing data the problem of estimating the period of a series of periodic events is considered under the condition where the measurements of the times of occurrence are noisy and sparse the problem is common to bit synchronisation in telecommunications and pulse train parameter estimation in electronic support among other applications two new algorithms are presented which represent different compromises between computational and statistical efficiency the first extends the separable least squares line search sls2 algorithms of sidiropoulos et al having very low computational complexity while attaining good statistical accuracy the second is an approximate maximum likelihood algorithm based on a low complexity lattice search and is found to achieve excellent accuracy

indirect dominant mode rejection a solution to low sample support beamforming under conditions of low sample support a low rank solution of the minimum variance distortionless response mvdr equations can yield a higher output signal to interference plus noise ratio sinr than the full rank mvdr beamformer in this paper we investigate several low rank beam forming techniques and we also propose a new beamformer that we refer to as the indirect dominant mode rejection idmr we analyze the degradation in the output sinr caused by residual cross correlations embedded in the sampled covariance matrix due to low sample support the idmr beamformer is based on a parametric estimate of the covariance matrix in which any cross correlation is canceled out simulations reveal that the idmr beamformer yields a dramatic improvement in output sinr relative to the conjugate gradient cg principal component inverse pci and dominant mode rejection dmr beamformers in our investigation of the low rank cg beamformer we address the issue of whether the unity gain constraint in the look direction should be enforced a priori via the use of a blocking matrix or effected a posteriori through simple scaling of the beamforming vector remarkably it is proven that the two methods yield exactly the same low rank beamformer at each and every rank

on the virtual array concept for higher order array processing for about two decades many fourth order fo array processing methods have been developed for both direction finding and blind identification of non gaussian signals one of the main interests in using fo cumulants only instead of second order so ones in array processing applications relies on the increase of both the effective aperture and the number of sensors of the considered array which eventually introduces the fo virtual array concept presented elsewhere and allows in particular a better resolution and the processing of more sources than sensors to still increase the resolution and the number of sources to be processed from a given array of sensors new families of blind identification source separation and direction finding methods at an order m 2q q spl ges 2 only have been developed recently in this context the purpose of this paper is to provide some important insights into the mechanisms and more particularly to both the resolution and the maximal processing capacity of numerous 2qth order array processing methods whose previous methods are part of by extending the virtual array concept to an arbitrary even order for several arrangements of the data statistics and for arrays with space angular and or polarization diversity

testing preorders for probabilistic processes can be characterized by simulations the domestic dog may be exceptionally well suited for behavioral genetic studies owing to its population history and the striking behavior differences among breeds to explore to what extent and ho

complex elliptically symmetric distributions survey new results and applications complex elliptically symmetric ces distributions have been widely used in various engineering applications for which non gaussian models are needed in this overview circular ces distributions are surveyed some new results are derived and their applications e g in radar and array signal processing are discussed and illustrated with theoretical examples simulations and analysis of real radar data the maximum likelihood ml estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness and for convergence of the iterative fixed point algorithm are established specific ml estimators for several ces distributions that are widely used in the signal processing literature are discussed in depth including the complex t distribution k distribution the generalized gaussian distribution and the closely related angular central gaussian distribution a generalization of ml estimators the m estimators of the scatter matrix are also discussed and asymptotic analysis is provided applications of ces distributions and the adaptive signal processors based on ml and m estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for direction of arrival doa estimation and beamforming furthermore experimental validation of the usefulness of ces distributions for modelling real radar data is given

principles of multivariate analysis a user s perspective part i looking at multivariate data part ii samples populations and models part iii analysing ungrouped data part iv analysing grouped data part v analysing association among variables appendix some basic matrix theory a1 definitions a2 elementary arithmetic operations a3 determinants and inverses a4 quadratic forms a5 latent roots and vectors a6 matrix square root a7 partitioned matrices a8 vector differentiation references index

subspace identification with eigenvalue constraints standard subspace methods for the identification of discrete time linear time invariant systems are transformed into generalized convex optimization problems in which the poles of the system estimate are constrained to lie within user defined convex regions of the complex plane the transformation is done by restating subspace methods such as the minimization of a frobenius norm affine in the estimate parameters allowing the minimization to be augmented with convex constraints the constraints are created using linear matrix inequality regions which generalize standard lyapunov stability to arbitrary convex regions of the complex plane the algorithm is developed for subspace methods based on estimates of the extended observability matrix and methods based on estimates of state sequences but it is extendable to all subspace methods simulation examples demonstrate the utility of the proposed method

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

steady state analysis of the multistage constant modulus array the multistage constant modulus cm array is a cascade adaptive beamforming system that can recover several narrowband cochannel signals without training we examine its steady state properties at convergence using a stochastic analysis and computer simulations based on a wiener model of convergence for the gradient adaptive algorithms closed form expressions are derived for the cm array and canceller weight vectors as well as the effective source direction vectors at all stages along the cascade system the signal capture and direction finding capabilities of the system are also discussed computer simulations for stationary and fading sources are presented to confirm the theoretical results and to illustrate the rapid convergence behavior of the adaptive algorithms

readies and failures in the algebra of communicating processes readiness and failure semantics are studied in the setting of algebra of communicating processes acp a model of process graphs modulo readiness equivalence respectively failure equivalence is constructed and an equational axiom system is presented which is complete for this graph model an explicit representation of the graph model is given the failure model whose elements are failure sets furthermore a characterisation of failure equivalence is obtained as the maximal congruence which is consistent with trace semantics by suitably restricting the communication format in acp this result is shown to carry over to subsets of hoare s communicating sequential processes csp and milner s calculus of communicating systems ccs also the characterisation implies a full abstraction result for the failure model in the above we restrict ourselves to finite processes without tau steps at the end of the paper a comment is made on the situation for infinite processes with tau steps notably w

branching bisimulation congruence for probabilistic systems a notion of branching bisimilarity for the alternating model of probabilistic systems compatible with parallel composition is defined for a congruence result an internal transition immediately followed by a non trivial probability distribution is not considered inert a weaker definition of branching bisimilarity for the same model has been given earlier here we show that our branching bisimulation is the coarsest congruence for parallel composition that is included in the weaker version to support the use of the present equivalence as a reduction technique we also show that probabilistic ctl formulae are preserved by our equivalence and we provide a polynomial time algorithm deciding branching bisimilarity

reactive generative and stratified models of probabilistic processes abstract we introduce three models of probabilistic processes namely reactive generative and stratified these models are investigated within the context of pccs an extension of milner s sccs in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1 for each model we present a structural operational semantics of pccs and a notion of bisimulation equivalence which we prove to be a congruence we also show that the models form a hierarchy the reactive model is derivable from the generative model by abstraction from the relative probabilities of different actions and the generative model is derivable from the stratified model by abstraction from the purely probabilistic branching structure moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities

doa estimation by exploiting the symmetric configuration of uniform linear array a new direction of arrival doa estimation method is proposed for uniform linear array in this paper when both uncorrelated and coherent sources are present the uncorrelated and coherent sources are estimated at two different stages the uncorrelated sources are first estimated using conventional subspace methods and then they are eliminated by exploiting the symmetric configuration of the array finally the remaining coherent sources are estimated by reconstructing a non toeplitz matrix the number of sources resolved by our method can exceed the number of array elements simulation results demonstrate the effectiveness and efficiency of our proposed method

orthogonal exactly periodic subspace decomposition the detection and estimation of machine vibration multiperiodic signals of unknown periods in white gaussian noise is investigated new estimates for the subsignals signals making up the received signal and their periods are derived using an orthogonal subspace decomposition approach the concept of exactly periodic signals is introduced this in turn simplifies and enhances the understanding of periodic signals

identification of positive real models in subspace identification by using regularization in time domain subspace methods for identifying linear time invariant dynamical systems the model matrices are typically estimated from least squares based on estimated kalman filter state sequences and the observed outputs and or inputs it is well known that for an infinite amount of data this least squares estimate of the system matrices is unbiased when the system order is correctly estimated however for a finite amount of data the obtained model may not be positive real in which case the algorithm is not able to identify a valid stochastic model in this note positive realness is imposed by adding a regularization term to a least squares cost function in the subspace identification algorithm the regularization term is the trace of a matrix which involves the dynamic system matrix and the output matrix

branching bisimulation for probabilistic systems characteristics and decidability we address the concept of abstraction in the setting of probabilistic reactive systems and study its formal underpinnings for the strictly alternating model of hansson in particular we define the notion of branching bisimilarity and study its properties by studying two other equivalence relations viz coloured trace equivalence and branching bisimilarity using maximal probabilities we show that both alternatives coincide with branching bisimilarity the alternative characterisations have their own merits and focus on different aspects of branching bisimilarity coloured trace equivalence can be understood without knowledge of probability theory and is independent of the notion of a scheduler branching bisimilarity rephrased in terms of maximal probabilities gives rise to an algorithm of polynomial complexity for deciding the equivalence together they give a better understanding of branching bisimilarity furthermore we show that the notions of branching bisimilarity in the alternating model of hansson and in the nonalternating model of segala differ branching bisimilarity in the latter setting turns out to discriminate between systems that are intuitively branching bisimilar

coprime sensing via chinese remaindering over quadratic fields part i array designs a coprime antenna array consists of two or more sparse subarrays featuring enhanced degrees of freedom dof and reduced mutual coupling this paper introduces a new class of planar coprime arrays based on the theory of ideal lattices in quadratic number fields a splitting prime p can be decomposed into the product of two distinct prime ideals which give rise to the two sparse subarrays their virtual difference coarray enjoys a quadratic gain in dof thanks to the generalized chinese remainder theorem crt to enlarge the contiguous aperture of the coarray we present hole free symmetric crt arrays with simple closed form expressions the ring of gaussian integers and the ring of eisenstein integers are considered as examples to demonstrate the procedure of designing coprime arrays with eisenstein integers our design yields a difference coarray that is a subset of the hexagonal lattice offering a significant gain in dof over the rectangular lattice given the same physical areas maximization of crt arrays in the aspect of essentialness and the superior performance in the context of angle estimation will be presented in the companion paper part ii

measuring correlations in symbol sequences abstract the paper is devoted to relations between correlation functions and mutual information it is shown that in sequences over an alphabet of symbols statistical dependences are measured by 1 2 independent parameters however not all of them can be determined by autocorrelation functions appropriate sets of correlation functions including crosscorrelations are introduced which allow the detection of all dependences the results are exemplified for binary ternary and quaternary symbol sequences as an application it is discussed that a nonuniform codon usage in protein coding dna sequences introduces periodic correlations even at distances in the order of 1000 base pairs

nested periodic matrices and dictionaries new signal representations for period estimation in this paper we propose a new class of techniques to identify periodicities in data we target the period estimation directly rather than inferring the period from the signal s spectrum by doing so we obtain several advantages over the traditional spectrum estimation techniques such as dft and music apart from estimating the unknown period of a signal we search for finer periodic structure within the given signal for instance it might be possible that the given periodic signal was actually a sum of signals with much smaller periods for example adding signals with periods 3 7 and 11 can give rise to a period 231 signal we propose methods to identify these hidden periods 3 7 and 11 we first propose a new family of square matrices called nested periodic matrices npms having several useful properties in the context of periodicity these include the dft walsh hadamard and ramanujan periodicity transform matrices as examples based on these matrices we develop high dimensional dictionary representations for periodic signals various optimization problems can be formulated to identify the periods of signals from such representations we propose an approach based on finding the least l 2 norm solution to an under determined linear system alternatively the period identification problem can also be formulated as a sparse vector recovery problem and we show that by a slight modification to the usual l 1 norm minimization techniques we can incorporate a number of new and computationally simple dictionaries

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

consistency and mse performance of music based doa of a single source in white noise with randomly missing data music is a popular algorithm for estimating the direction of arrival doa in array signal processing applications in this paper we analyze the performance of the music algorithm for a single source system in the presence of noisy and missing data when only a random subset of the entries in the data matrix are observed we prove consistency of the doa estimate when signal from a single source is impinging on low coherence arrays and derive an analytic expression for the mean squared error mse performance of music for the case of uniform linear arrays in the large array and relatively large sample setting our analysis is mathematically justified in both the sample rich and deficient regimes the expression for the mse is a simple function of array geometry signal to noise ratio snr the fraction of entries observed and the ratio of the number of sensors to number of snapshots we derive a phase transition threshold which separates a regime where music is consistent from a regime where music is inconsistent this threshold depends upon the snr the probability of observing entries in the data matrix and number of sensors and snapshots in a simple manner which we make explicit

orthogonal and non orthogonal signal representations using new transformation matrices having npm structure in this article we introduce two types of real valued sums known as complex conjugate pair sums ccpss denoted as ccps 1 and ccps 2 and discuss a few of their properties using each type of ccpss and their circular shifts we construct two non orthogonal nested periodic matrices npms as npms are non singular this introduces two non orthogonal transforms known as complex conjugate periodic transforms ccpts denoted as ccpt 1 and ccpt 2 we propose another npm which uses both types of ccpss such that its columns are mutually orthogonal this transform is known as orthogonal ccpt occpt after a brief study of a few occpt properties like periodicity circular shift etc we present two different interpretations of it further we propose a decimation in time dit based fast computation algorithm for occpt termed as foccpt whenever the length of the signal is equal to 2 v v in mathbb n the proposed sums and transforms are inspired by ramanujan sums and ramanujan period transform rpt finally we show that the period both divisor and non divisor and frequency information of a signal can be estimated using the proposed transforms with a significant reduction in the computational complexity over discrete fourier transform dft

estimating periodicities in symbolic sequences using sparse modeling in this paper we propose a method for estimating statistical periodicities in symbolic sequences different from other common approaches used for the estimation of periodicities of sequences of arbitrary finite symbol sets that often map the symbolic sequence to a numerical representation we here exploit a likelihood based formulation in a sparse modeling framework to represent the periodic behavior of the sequence the resulting criterion includes a restriction on the cardinality of the solution two approximate solutions are suggested one greedy and one using an iterative convex relaxation strategy to ease the cardinality restriction the performance of the proposed methods are illustrated using both simulated and real dna data showing a notable performance gain as compared to other common estimators

subspace identification with guaranteed stability using constrained optimization in system identification the true system is often known to be stable however due to finite sample constraints modeling errors plant disturbances and measurement noise the identified model may be unstable we present a constrained optimization method to ensure asymptotic stability of the identified model in the context of subspace identification methods in subspace identification we first obtain an estimate of the state sequence or extended observability matrix and then solve a least squares optimization problem to estimate the system parameters to ensure asymptotic stability of the identified model we write the least squares optimization problem as a convex linear programming problem with mixed equality quadratic and positive semidefinite constraints suitable for existing convex optimization codes such as sedumi we present examples to illustrate the method and compare to existing approaches

ramanujan fourier series the wiener khintchine formula and the distribution of prime pairs the wiener khintchine formula plays a central role in statistical mechanics it is shown here that the problem of prime pairs is related to autocorrelation and hence to a wiener khintchine formula experimental evidence is given for this c 1999 elsevier science b v all rights reserved

a two stage method for inverse medium scattering we present a novel numerical method to the time harmonic inverse medium scattering problem of recovering the refractive index from noisy near field scattered data the approach consists of two stages one pruning step of detecting the scatterer support and one resolution enhancing step with nonsmooth mixed regularization the first step is strictly direct and of sampling type and it faithfully detects the scatterer support the second step is an innovative application of nonsmooth mixed regularization and it accurately resolves the scatterer size as well as intensities the nonsmooth model can be efficiently solved by a semi smooth newton type method numerical results for two and three dimensional examples indicate that the new approach is accurate computationally efficient and robust with respect to data noise

observing branching structure through probabilistic contexts probabilistic automata pas constitute a general framework for modeling and analyzing discrete event systems that exhibit both nondeterministic and probabilistic behavior such as distributed algorithms and network protocols the behavior of pas is commonly defined using schedulers also called adversaries or strategies which resolve all nondeterministic choices based on past history from the resulting purely probabilistic structures trace distributions can be extracted whose intent is to capture the observable behavior of a pa however when pas are composed via an asynchronous parallel composition operator a global scheduler may establish strong correlations between the behavior of system components and for example resolve nondeterministic choices in one pa based on the outcome of probabilistic choices in the other it is well known that as a result of this the linear time trace distribution precongruence is not compositional for pas in his 1995 ph d thesis segala has shown that the branching time probabilistic simulation preorder is compositional for pas in this paper we establish that the simulation preorder is in fact the coarsest refinement of the trace distribution preorder that is compositional we prove our characterization result by providing 1 a context of a given pa cal a called the tester which may announce the state of cal a to the outside world and 2 a specific global scheduler called the observer which ensures that the state information that is announced is actually correct now when another pa cal b is composed with the tester it may generate the same external behavior as the observer only when it is able to simulate cal a in the sense that whenever cal a goes to some state s cal b can go to a corresponding state u from which it may generate the same external behavior our result shows that probabilistic contexts together with global schedulers are able to exhibit the branching structure of pas

a hierarchy of probabilistic system types we arrange various classes of probabilistic systems studied in the literature in an expressiveness hierarchy our expressiveness criterion is the existence of a system translation from the less expressive type into the more expressive type that preserves and reflects probabilistic bisimilarity we model the different system types as coalgebras of suitable behaviour functors and argue that the corresponding coalgebraic bisimilarity coincides with probabilistic bisimilarity for the classes for which the latter notion has been proposed in the literature the theory of coalgebras provides a unified framework for the presentation of the different classes and the system translations we needed to establish the hierarchy all these translations arise in a standard way from natural transformations between the two behaviour functors involved such a translation generally preserves coalgebraic bisimilarity we exploit a new result that under mild assumptions on the behaviour functors a system translation induced by a natural transformation with injective components also reflects bisimilarity

signal processing applications of oblique projection operators oblique projection operators are used to project measurements onto a low rank subspace along a direction that is oblique to the subspace they may be used to enhance signals while nulling interferences in the paper the authors give several basic results for oblique projections including formulas for constructing oblique projections with desired range and null space they analyze the algebra and geometry of oblique projections in order to understand their properties they then show how oblique projections can be used to separate signals from structured noise such as impulse noise damped or undamped interfering sinusoids such as power line interference and narrow band noise in some of the problems addressed the oblique projection provides an alternative way to implement an already known solution expressing these solutions as oblique projections brings geometrical insight to the study of the solution the geometry of oblique projections enables one to compute performance in terms of angles between signal and noise subspaces as a special case of removing impulse noise the authors can use oblique projections to interpolate missing data samples in array processing oblique projections can be used to simultaneously steer beams and nulls in communications oblique projections can be used to remove intersymbol interference

logical characterization of branching metrics for nondeterministic probabilistic transition systems abstract in this paper we propose a logical characterization of bi simulation metrics obtained by a probabilistic variant of hennessy milner logic enriched with variables whose semantics is defined following the equational calculus approach our characterization is based on the novel notions of mimicking formulae and syntactical distance on formulae the former ones are the quantitative analogous to characteristic formulae the latter is a 1 bounded pseudometric on formulae measuring their syntactical disparities the characterization is obtained by showing that the bi simulation distance between processes corresponds to the syntactical distance between their mimicking formulae we also discuss the expressive power of mimicking formulae with respect to probabilistic bi simulations we show that two processes are bisimilar if and only if their mimicking formulae are syntactically equivalent moreover we obtain that mimicking formulae of processes coincide with their characteristic formulae for ready simulation and that negation free mimicking formulae coincide with the characteristic formulae for simulation

signal periodic decomposition with conjugate subspaces in this paper we focus on hidden period identification and the periodic decomposition of signals based on recent results on the ramanujan subspace we reveal the conjugate symmetry of the ramanujan subspace with a set of complex exponential basis functions and represent the subspace as the union of a series of conjugate subspaces with these conjugate subspaces the signal periodic model is introduced to characterize the periodic structure of a signal to achieve the decomposition of the proposed model conjugate subspace pursuit with periodicity and energy csppe algorithm is proposed based on two different greedy strategies the csppe is performed iteratively in two stages in the first stage the dominant hidden period is chosen with the periodicity strategy then the dominant conjugate subspace is chosen with the energy strategy in the second stage compared with the current state of the art methods for hidden period identification the main advantages provided by the csppe are the following 1 the capability of identifying all the hidden periods in the range from 1 to the maximum hidden period q of a signal of any length without truncating the signal 2 the ability to identify the time varying hidden period with its shifted version and 3 the low computational cost without generating and using a large over complete dictionary moreover we provide examples and applications to demonstrate the abilities of the proposed two stage csppe algorithm which include hidden period identification signal approximation time varying period detection and pitch detection of speech

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

performance analysis of spatial smoothing with interpolated arrays the interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival doas of signals some of which may be perfectly correlated it extends the spatial smoothing method to arbitrary array geometries a statistical performance analysis of the algorithm is presented closed form expressions for the covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluating these expressions for specific cases and comparing them to the cramer rao lower bound for the doa estimates provides insight into the statistical efficiency of this algorithm the formulas for the error covariance are quite general and can be specialized to provide results for other doa estimation algorithms as well

application of information theory to dna sequence analysis a review the analysis of dna sequences through information theory methods is reviewed from the beginning in the 70s the subject is addressed within a broad context describing in some detail the cornerstone contributions in the field the emerging interest concerning long range correlations and the mosaic structure of dna sequences is considered from our own point of view a recent procedure developed by the authors is also outlined

maximum likelihood identification of stable linear dynamical systems this paper concerns maximum likelihood identification of linear time invariant state space models subject to model stability constraints we combine expectation maximization em and lagrangian re

convolution idempotents with a given zero set we investigate the structure of n length discrete signals h satisfying h h h that vanish on a given set of indices we motivate this problem from examples in sampling fuglede s conjecture and orthogonal interpolation of bandlimited signals when n p m is a prime power we characterize all such h with a prescribed zero set in terms of base p expansions of nonzero indices in mathcal f 1 h

cyclo period estimation for discrete time cyclo stationary signals this paper presents a new method named as the variability method to estimate the cyclo period of a discrete time cyclo stationary signal the method is essentially based on the time varying correlation and or the time varying mean whose estimators are associated with some statistics of blocked signals a plot of variability of these statistics as a function of the blocking operator index visually reveals a periodic pattern from which the cyclo period is obtained properties of the variability method are analyzed and compared with three existing cyclo period estimation methods via simulation and real life examples

orthogonal ramanujan sums its properties and applications in multiresolution analysis signal processing community has recently shown interest in ramanujan sums which were defined by s ramanujan in 1918 in this paper we propose a family of sequences termed here as orthogonal ramanujan sums c k q n and also derive their various properties we also prove two new properties of the ramanujan sums namely shifted multiplication property and interpolation property these properties are used to define higher order orthogonal ramanujan sums these sums are periodic in nature and are orthogonal for different values of k and q using orthogonal ramanujan sums a new representation of finite length signal is given termed here as orthogonal ramanujan periodic transform the coefficients obtained using this transform can be divided into two parts first coefficient gives smoothing component and the rest give the detail components of the signal further application of the orthogonal ramanujan sums in discrete wavelet transform is developed construction of ramanujan wavelet analysis matrix for applying discrete wavelet transform on a signal is described the application of this matrix on an image of size n times n where n is divisible by integer q will result in q 2 1 detail components and one average component in transform domain some of the applications of this transform are also demonstrated especially in the field of image processing

bounded gaps between primes it is proved that lim inf n 8 p n 1 p n 7 10 7 where p n is the n th prime our method is a refinement of the recent work of goldston pintz and yildirim on the small gaps between consecutive primes a major ingredient of the proof is a stronger version of the bombieri vinogradov theorem that is applicable when the moduli are free from large prime divisors only but it is adequate for our purpose

periodicity transforms this paper presents a method of detecting periodicities in data that exploits a series of projections onto periodic subspaces the algorithm finds its own set of nonorthogonal basis elements based on the data rather than assuming a fixed predetermined basis as in the fourier gabor and wavelet transforms a major strength of the approach is that it is linear in period rather than linear in frequency or linear in scale the algorithm is derived and analyzed and its output is compared to that of the fourier transform in a number of examples one application is the finding and grouping of rhythms in a musical score another is the separation of periodic waveforms with overlapping spectra and a third is the finding of patterns in astronomical data examples demonstrate both the strengths and weaknesses of the method

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

identification of stable models in subspace identification by using regularization in subspace identification methods the system matrices are usually estimated by least squares based on estimated kalman filter state sequences and the observed inputs and outputs for a finite number of data points the estimated system matrix is not guaranteed to be stable even when the true linear system is known to be stable in this paper stability is imposed by using regularization the regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive semi definite weighting matrix the amount of regularization can be determined from a generalized eigenvalue problem the data augmentation method of chui and maciejowski 1996 is obtained by using specific choices for the weighting matrix in the regularization term

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

performance analysis of the enhanced minimum variance spatial spectrum estimator the performance of the enhanced minimum variance emv spatial spectrum estimator is studied expressions are presented fur the variance and bias of direction of arrival estimators based on general functions of the covariance matrix and these expressions are then used to study the emv estimator finite data effects and random perturbations on the ideal modeling assumptions are studied separately

solving the protein sequence metric problem biological sequences are composed of long strings of alphabetic letters rather than arrays of numerical values lack of a natural underlying metric for comparing such alphabetic data significantly inhibits sophisticated statistical analyses of sequences modeling structural and functional aspects of proteins and related problems herein we use multivariate statistical analyses on almost 500 amino acid attributes to produce a small set of highly interpretable numeric patterns of amino acid variability these high dimensional attribute data are summarized by five multidimensional patterns of attribute covariation that reflect polarity secondary structure molecular volume codon diversity and electrostatic charge numerical scores for each amino acid then transform amino acid sequences for statistical analyses relationships between transformed data and amino acid substitution matrices show significant associations for polarity and codon diversity scores transformed alphabetic data are used in analysis of variance and discriminant analysis to study dna binding in the basic helix loop helix proteins the transformed scores offer a general solution for analyzing a wide variety of sequence analysis problems

ramanujan sums in the context of signal processing part ii fir representations and applications the mathematician ramanujan introduced a summation in 1918 now known as the ramanujan sum c q n in a companion paper part i properties of ramanujan sums were reviewed and ramanujan subspaces s q introduced of which the ramanujan sum is a member in this paper the problem of representing finite duration fir signals based on ramanujan sums and spaces is considered first it is shown that the traditional way to solve for the expansion coefficients in the ramanujan sum expansion does not work in the fir case two solutions are then developed the first one is based on a linear combination of the first n ramanujan sums with n being the length of the signal the second solution is based on ramanujan subspaces with q 1 q 2 q k denoting the divisors of n it is shown that x n can be written as a sum of k signals x qi n s qi furthermore the i th signal x qi n has period q i and any pair of these periodic components is orthogonal the components x qi n can be calculated as orthogonal projections of x n onto ramanujan spaces s qi then the ramanujan periodic transform rpt is defined based on this and is useful to identify hidden periodicities it is shown that the projection matrices which compute x qi n from x n are integer matrices except for an overall scale factor the calculation of projections is therefore rendered easy to estimate internal periods n n of x n one only needs to know which projection energies are nonzero

two dimensional efficient multiplier less structures of mobius function for ramanujan filter banks ramanujan s sum has been recently applied to detect different periodic components in 2d image by filtering in frequency domain and obtaining the least common multiplier lcm of periodicity matrices the basic 2d periodic pattern can be found this paper introduces a multiplier less structure to efficiently implement this process based on the well known number theoretic function called mobius function the relationship between impulse train and ramanujan s sum is also clearly described in both 1d and 2d cases

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

kalman based estimator for doa estimations we introduce a new kalman based noise subspace estimator combined with the root music for direction of arrival doa estimation of uncorrelated narrow band plane waves impinging on an array of sensors without both a priori knowledge of the number of sources and the inflation method presented by yang and kaveh 1988 we show that the kalman based estimator can approximately estimate the complete noise subspace with small bias for high input signal to noise ratio snr scenario the proposed algorithm needs slightly more computation operations per adaptive cycle than yang and kaveh s lms based algorithm but with much more rapid convergence simulations demonstrate the effectiveness of the proposed algorithm

a unified theory of union of subspaces representations for period estimation several popular period estimation techniques use union of subspaces models to represent periodic signals the main idea behind these techniques is to compare the components of the signal along a set of subspaces representing different periods such techniques were shown to offer important advantages over traditional methods such as those based on dft so far most of these subspace techniques have been developed independent of each other and there has not been a unified theory analyzing them from a common perspective in this paper all such methods are first unified under one general framework further several fundamental aspects of such subspaces are investigated such as the conditions under which a generic set of subspaces offers unique periodic decompositions their minimum required dimensions etc a number of basic questions in the context of dictionaries spanning periodic signals are also answered for example what is the theoretically minimum number of atoms required in any type of dictionary in order to be able to represent periods 1 p p max for each period p what should be the minimum dimension of the subspace of atoms representing the pth period itself unlike in traditional fourier dictionaries it is shown that nonuniform and compact grids are crucial for period estimation interestingly it will be seen that the euler totient function from number theory plays an important role in providing the answers to all such questions

adaptive comb filtering for harmonic signal enhancement a new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise the algorithm is composed of two cascaded parts the first estimates the fundamental frequency and enhances the harmonic component in the input and the second estimates the harmonic amplitudes and phases performance analysis provides new results for the asymptotic cramer rao bound crb on the parameters of harmonic signals with additive white noise results of simulations indicate that the variances of the estimates are of the same order of magnitude as the crb for sufficiently large data sets and illustrate the performance in enhancing noisy artificial periodic signals

multidimensional inverse lattice problem and a uniformly sampled arithmetic fourier transform the present work develops a unified and concise solution for inverse lattice problems also a uniformly sampled arithmetic fourier transform is presented in this work which uses ramanujan s sum rule

analytical performance assessment of multi dimensional matrix and tensor based esprit type algorithms in this paper we present a generic framework for the asymptotic performance analysis of subspace based parameter estimation schemes it is based on earlier results on an explicit first order expansion of the estimation error in the signal subspace obtained via an svd of the noisy observation matrix we extend these results in a number of aspects firstly we demonstrate that an explicit first order expansion of the higher order svd hosvd based subspace estimate can be derived secondly we show how to obtain explicit first order expansions of the estimation error of arbitrary esprit type algorithms and provide the expressions for r d standard esprit r d unitary esprit r d standard tensor esprit as well as r d unitary tensor esprit thirdly we derive closed form expressions for the mean square error mse and show that they only depend on the second order moments of the noise hence to apply this framework we only need the noise to be zero mean and possess finite second order moments additional assumptions such as gaussianity or circular symmetry are not needed

ramanujan sums in the context of signal processing part i fundamentals the famous mathematician s ramanujan introduced a summation in 1918 now known as the ramanujan sum c q n for any fixed integer q this is a sequence in n with periodicity q ramanujan showed that many standard arithmetic functions in the theory of numbers such as euler s totient function n and the mobius function n can be expressed as linear combinations of c q n 1 q in the last ten years ramanujan sums have aroused some interest in signal processing there is evidence that these sums can be used to extract periodic components in discrete time signals the purpose of this paper and the companion paper part ii is to develop this theory in detail after a brief review of the properties of ramanujan sums the paper introduces a subspace called the ramanujan subspace s q and studies its properties in detail for fixed q the subspace s q includes an entire family of signals with properties similar to c q n these subspaces have a simple integer basis defined in terms of the ramanujan sum c q n and its circular shifts the projection of arbitrary signals onto these subspaces can be calculated using only integer operations linear combinations of signals belonging to two or more such subspaces follows certain specific periodicity patterns which makes it easy to identify periods in the companion paper part ii it is shown that arbitrary finite duration signals can be decomposed into a finite sum of orthogonal projections onto ramanujan subspaces

subspace leakage analysis and improved doa estimation with small sample size classical methods of doa estimation such as the music algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix for a small number of samples such methods are exposed to performance breakdown as the sample covariance matrix can largely deviate from the true covariance matrix in this paper the problem of doa estimation performance breakdown is investigated we consider the structure of the sample covariance matrix and the dynamics of the root music algorithm the performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace in this paper the subspace leakage is theoretically derived we also propose a two step method that improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced furthermore we introduce a phenomenon named as root swap which occurs in the root music algorithm in the low sample size region and degrades the performance of the doa estimation a new method is then proposed to alleviate this problem numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods moreover the proposed algorithms are combined with the pseudo noise resampling method to further improve the performance