estimating the parameters of chirp signals an iterative approach this correspondence is concerned with the problem of estimating the parameters of constant amplitude chirp signals embedded in noise an estimation algorithm based on a simple iterative approach is proposed whose main characteristics include accuracy reduction in the error propagation effect and operation over a wide range of phase parameter values the estimation is quite robust against additive noise and is shown to achieve the cramer rao lower bound even at relatively low signal to noise ratios simulation results are presented that justify the viability of the new algorithm and demonstrate its better performance as compared with the existing techniques

parameter estimation of chirp signals the problem of the parameter estimation of chirp signals is addressed several closely related estimators are proposed whose main characteristics are simplicity accuracy and ease of online or offline implementation for moderately high signal to noise ratios they are unbiased and attain the cramer rao bound monte carlo simulations verify the expected performance of the estimators it should be easy to extend this approach to signals having polynomials of any degree in the exponent all the derivations will be done under the assumption that the signal to noise ratio is sufficiently high

discrete time local polynomial approximation of the instantaneous frequency the local polynomial approximation lpa of the time varying phase is used to develop a new form of the fourier transform and the local polynomial periodogram lpp as an estimator of the instantaneous frequency if spl omega t of a harmonic complex valued signal the lpp is interpreted as a time frequency energy distribution over the t spl omega t spl omega sup 1 t spl omega sup m 1 t space where m is a degree of the lpa the variance and bias of the estimate are studied for the short and long time asymptotic behavior of the if estimates in particular it is shown that the optimal asymptotic mean squared errors of the estimates of spl omega sup k 1 t have orders o n sup 2k 1 and o n sup 2 m k 1 2m 3 k 1 2 m respectively for a polynomial spl omega t of the degree m 1 and arbitrary smooth spl omega t with a bounded mth derivative

h measures a new approach for studying homogenisation oscillations and concentration effects in partial differential equations new mathematical objects called h measures are introduced for studying oscillations and concentration effects in partial differential equations applications to transport properties and to homogenisation are given as an example of the new results which can be obtained by this approach

an analytical characterization of effective and of irreducible groups inducing cone orderings abstract an analytical characterization of effective and of irreducible groups inducing cone orderings is given the characterization implies easily a necessary condition for a group majorization to be a group induced cone ordering

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

g invariant norms and g c radii abstract let v be a finite dimensional inner product space over f r or c and let g be a closed subgroup of the group of unitary operators on v a norm or a seminorm on v is said to be g invariant if g x x for all g g x v the concept of g invariant norm specializes to many interesting particular cases such as the absolute norms on f n symmetric gauge functions on r n unitarily invariant norms on f m n etc which are of wide research interest in this paper we study the general properties of g invariant norms our main strategy is to study g invariant norms via the g c radius rg c on v defined by r g c x max x g c g g where c v it is shown that the g c radii are very important g invariant seminorms because every g invariant norm or seminorm admits a representation in terms of them as a result one may focus attention on g c radii in order to get results on g invariant norms we study the norm properties of g c radii and obtain various results relating g invariant norms and g c radii the linear operators on v that preserve g invariant norms g invariant seminorms or g c radii are also investigated several open questions are mentioned

decay of periodic entropy solutions to degenerate nonlinear parabolic equations abstract under a precise nonlinearity diffusivity condition we establish the decay of space periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation

estimation and classification of polynomial phase signals the measurement of the parameters of complex signals with constant amplitude and polynomial phase measured in additive noise is considered a novel new integral transform that is adapted for signals of this type is introduced this transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance the algorithms are extended to constant amplitude and continuous nonpolynomial phase signals

group majorization and schur type inequalities abstract the problem of the reduction of a group majorization induced by an infinite group to a finite group majorization is discussed a necessary and sufficient condition for a possibility of the reduction is given the condition generalizes some known inequalities in the matrix theory involving eigenvalues or singular values of a matrix a corresponding result for a skew symmetric matrix is derived

discrete chirp fourier transform and its application to chirp rate estimation the discrete fourier transform dft has found tremendous applications in almost all fields mainly because it can be used to match the multiple frequencies of a stationary signal with multiple harmonics in many applications wideband and nonstationary signals however often occur one of the typical examples of such signals is chirp type signals that are usually encountered in radar signal processing such as synthetic aperture radar sar and inverse sar imaging due to the motion of a target the radar return signals are usually chirps and their chirp rates include the information about the target such as the location and the velocity in this paper we study discrete chirp fourier transform dcft which is analogous to the dft besides the multiple frequency matching similar to the dft the dcft can be used to match the multiple chirp rates in a chirp type signal with multiple chirp components we show that when the signal length n is prime the magnitudes of all the sidelobes of the dcft of a quadratic chirp signal are 1 whereas the magnitude of the mainlobe of the dcft is spl radic n with this result an upper bound for the number of the detectable chirp components using the dcft is provided in terms of signal length and signal and noise powers we also show that the n point dcft performs optimally when n is a prime

on svd for estimating generalized eigenvalues of singular matrix pencil in noise several algorithms for estimating generalized eigenvalues ges of singular matrix pencils perturbed by noise are reviewed the singular value decomposition svd is explored as the common structure in the three basic algorithms direct matrix pencil algorithm pro esprit and tls esprit it is shown that several svd based steps inherent in the algorithms are equivalent to the first order approximation in particular the pro esprit and its variant tls pro esprit are shown to be equivalent and the tls esprit and its earlier version ls esprit are shown to be asymptotically equivalent to the first order approximation for the problem of estimating superimposed complex exponential signals the state space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first order approximation the second order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal an improved state space algorithm is found to be the most robust to noise

joint model order selection and parameter estimation of chirps with harmonic components we consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp and estimating its parameters i e its initial frequency and frequency rate given time samples of the observed signal common model order criteria select the number of harmonics based on the maximum likelihood estimator we develop exact and approximated maximum likelihood estimators of these parameters to avoid an exhaustive search in the initial frequency frequency rate space involved by those estimators we propose an alternative low complexity two step estimation method the first step separates the signal to its harmonic components then in the second step the parameters of interest are estimated using least squares method given the phases of the harmonic components the method is compared to the exact and approximated maximum likelihood estimators and to the well known high order ambiguity function based method numerical simulations and real data examples demonstrate that the proposed low complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal to noise ratio since the estimates obtained by the proposed method achieve the cramer rao lower bound at these signal to noise ratios

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

an extension of schur ostrowski s condition weak eaton triples and generalized ai functions abstract in this paper for a given eaton triple v g d we present a characterization of g increasing real functions by using the maximality property of their directional derivatives it generalizes schur ostrowski s condition related to schur convexity of a function it is also useful in establishing theorems of von neumann davis type regarding the form of group invariant real functions with certain kinds of convexity we introduce and investigate weak eaton triples and their chains we show a method for constructing new eaton triples we apply it to define generalized arrangement increasing ai functions we prove that the mentioned derivatives of g increasing maps are generalized ai functions

estimating the doa and the polarization of a polynomial phase signal using a single polarized vector sensor this paper introduces a novel algorithm to estimate the direction of arrival doa and the polarization of a completely polarized polynomial phase signal of an arbitrary degree the algorithm utilizes a polarized vector sensor comprising a spatially collocated six component electromagnetic vector sensor a dipole triad or a loop triad this esprit based algorithm is based on a time invariant matrix pencil pair derived from the time delayed data sets collected by a single polarized vector sensor the high order difference function of the signal s phase constructs the invariant factor used in the esprit algorithm the steering vector is estimated from the signal subspace eigenvector of the data correlation matrix following which the closed form doa and polarization can be obtained given the degree of the polynomial phase signal this approach resolves the two dimensional azimuth elevation angle and the polarization of the source and requires neither a priori knowledge of the polynomial phase signal s coefficients nor a priori knowledge of the polynomial phase signal s frequency spectrum the efficacy of the proposed algorithm is verified by monte carlo simulations estimation accuracies of the doa and the polarization parameters are evaluated by the closed form cramer rao bounds which are independent of the polynomial coefficients the degree of the polynomial phase signal and the azimuth angle of the source

the cramer rao lower bound for signals with constant amplitude and polynomial phase the authors derive the cramer rao lower bound crlb for complex signals with constant amplitude and polynomial phase measured in additive gaussian white noise the exact bound requires numerical inversion of an ill conditioned matrix while its o n sup 1 approximation is free of matrix inversion the approximation is tested for several typical parameter values and is found to be excellent in most cases the formulas derived are of practical value in several radar applications such as electronic intelligence systems elint for special pulse compression radars and motion estimation from doppler measurements consequently it is of interest to analyze the best possible performance of potential estimators of the phase coefficients as a function of signal parameters the signal to noise ratio the sampling rate and the number of measurements this analysis is carried out

on g invariant norms abstract a result of r mathias and horn cf linear algebra appl 142 1990 63 on the representation of the unitarily invariant norm is extended in the context of eaton triples and of real semisimple lie algebras the representation is related to a function criteria for being a norm is given in terms of and the longest element of the underlying finite reflection group in particular for the real simple lie algebras is a norm on its cartan subspace for a given nonzero if and only if 0 where 0 is the longest element of the weyl group this is the case if the weyl group contains id some related results are obtained

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

entropy solutions for nonlinear degenerate problems we consider a class of elliptic hyperbolic degenerate equations g u delta b u divg phi u f with dirichlet homogeneous boundary conditions and a class of elliptic parabolic hyperbolic degenerate equations g u t delta b u divg phi u f with homogeneous dirichlet conditions and initial conditions existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function satisfying rather general conditions comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for continuous

affine images of riemannian manifolds we describe all affine maps from a riemannian manifold to a metric space and all possible image spaces

decay of entropy solutions of nonlinear conservation laws we are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws the main objective of this paper is to present an analytical approach and to explore its applications to studying the large time behavior of periodic entropy solutions of hyperbolic conservation laws the asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an important nonlinear phenomenon it is observed that the genuine nonlinearity of equations forces the waves of each characteristic family to interact vigorously and to cancel each other the insightful analysis of glimm lax gl for scalar equations and 2 2 systems has indicated that the resultant mutual cancellation of interacting shock and rarefaction waves of the same family induces the decay of periodic solutions such a result was first shown by lax l1 in 1957 for one dimensional convex scalar conservation laws dafermos d1 applying his uniform processes proved the decay result for the case that the set of inflection points of the flux does not have an accumulation point the glimm lax theory gl indicates that for 2 2 strictly hyperbolic and genuinely nonlinear systems any periodic glimm solution decays like o 1 t this result was proved by using the approximate characteristic method in the glimm difference solutions provided that the oscillation of the corresponding initial data is small recently using the method of generalized characteristics dafermos d3 showed that any periodic solution with local bounded variation and small oscillation for 2 2 systems decays asymptotically with the same detailed structure pas found by lax l1 for the

estimating random amplitude polynomial phase signals a cyclostationary approach modeling of a class of nonstationary signals with randomly time varying amplitude and parametric polynomial phase is addressed a novel approach is proposed for the estimation of the time varying phase by exploiting the higher order cyclostationarity of these signals the method does not require nonlinear search is easy to implement and yields consistent estimates for the parameters the resulting algorithms are theoretically tolerant to a large class of noises including additive stationary non gaussian noise and any gaussian noise simulation examples supporting the theory are provided

erratum to existence and strong pre compactness properties for entropy solutions of a first order quasilinear equation with discontinuous flux sequences of entropy solutions of a non degenerate first order quasilinear equation are shown to be strongly pre compact in the general case of a caratheodory flux vector existence of the weak and entropy solution to the cauchy problem for such an evolutionary equation is also established the proofs are based on the general localization principle for h measures corresponding to sequences of measure valued functions

cauchy schwarz inequalities associated with positive semidefinite matrices abstract using a quasilinear representation for unitarily invariant norms we prove a basic inequality let a l x x m be positive semidefinite where x m m n then x p 2 l p m p for all p 0 and all unitarily invariant norms we show how several inequalities of cauchy schwarz type follow from this bound and obtain a partial analog of our results for l p norms

on polynomial phase signals with time varying amplitudes we address the parameter estimation problem for a class of nonstationary signals modeled as polynomial phase signals with time varying amplitudes exponentially damped polynomial phase signals are treated as a special case and are analyzed in detail high order instantaneous moments provide the basic analytical tool but links are shown to exist with either the usually employed fft based technique or the high resolution kumaresan tufts 1982 music and matrix pencil methods asymptotic properties of the relevant estimators are established cramer rao lower bounds on the amplitude and phase parameter estimates are derived and computer simulations are carried out to evaluate the performance of various schemes we focus on parametric modeling of am fm signals mainly because parametric techniques offer parsimony and allow for theoretically unlimited resolution