ma estimation in polynomial time the parameter estimation of moving average ma signals from second order statistics was deemed for a long time to be a difficult nonlinear problem for which no computationally convenient and reliable solution was possible we show how the problem of ma parameter estimation from sample covariances can be formulated as a semidefinite program that can be solved in a time that is a polynomial function of the ma order two methods are proposed that rely on two specific over parametrizations of the ma covariance sequence whose use makes the minimization of a covariance fitting criterion a convex problem the ma estimation algorithms proposed here are computationally fast statistically accurate and reliable none of the previously available algorithms for ma estimation methods based on higher order statistics included shares all these desirable properties our methods can also be used to obtain the optimal least squares approximant of an invalid estimated ma spectrum that takes on negative values at some frequencies which was another long standing problem in the signal processing literature awaiting a satisfactory solution

optimal design of magnitude responses of rational infinite impulse response filters this correspondence considers a design of magnitude responses of optimal rational infinite impulse response iir filters the design problem is formulated as an optimization problem in which a total weighted absolute error in the passband and stopband of the filters the error function reflects a ripple square magnitude is minimized subject to the specification on this weighted absolute error function defined in the corresponding passband and stopband as well as the stability condition since the cost function is nonsmooth and nonconvex while the constraints are continuous this kind of optimization problem is a nonsmooth nonconvex continuous functional constrained problem to address this issue our previous proposed constraint transcription method is applied to transform the continuous functional constraints to equality constraints then the nonsmooth problem is approximated by a sequence of smooth problems and solved via a hybrid global optimization method the solutions obtained from these smooth problems converge to the global optimal solution of the original optimization problem hence small transition bandwidth filters can be obtained

a sequential partial optimization algorithm for minimax design of separable denominator 2 d iir filters a sequential partial optimization method is presented in this paper for the minimax design of two dimensional infinite impulse response filters with separable denominator the method converts the minimax design problem into a sequence of smaller subproblems each updating only one pair of second order denominator factors the necessary and sufficient stability triangles for one dimensional filters are used as the stability constraints on the two dimensional filters the first order taylor expansion and a trust region method are used to deal with the nonconvexity of the subproblems and guarantee the convergence of the solution algorithm by comparing with a corresponding joint optimization method the sequential partial optimization algorithm is shown to converge faster for filters with relatively high denominator order this is mainly due to the observation that the trust region to assure the convergence is usually much smaller for the joint optimization method moreover the limit solution of the sequential partial optimization algorithm has been proved to be a karush kuhn tucker point of the design problem design examples demonstrate that the proposed algorithm has obtained smaller maximum frequency response errors than the competing methods both for filters with separable denominator of the same order and for filters with nonseparable denominator of about the same implementation complexity

calderon zygmund estimates and non uniformly elliptic operators abstract we consider a class of non uniformly nonlinear elliptic equations whose model is given by div d u p 2 d u a x d u q 2 d u div f p 2 f a x f q 2 f where p q and a x 0 and establish the related nonlinear calderon zygmund theory in particular we provide sharp conditions under which the natural and optimal calderon zygmund type result f p a x f q l loc d u p a x d u q l loc holds for every 1 these problems naturally emerge as euler lagrange equations of some variational integrals introduced and studied by marcellini 41 and zhikov 53 in the framework of homogenisation and lavrentiev phenomenon

rounding effects of quenched randomness on first order phase transitions frozen in disorder in an otherwise homogeneous system is modeled by interaction terms with random coefficients given by independent random variables with a translation invariant distribution for such systems it is proven that ind 2 dimensions there can be no first order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter discontinuities which would amount to a continuous symmetry breaking in systems which are stochastically invariant under the action of a continuous subgroup ofo n are suppressed by the randomness in dimensionsd 4 specific implications are found in the random field ising model for which we conclude that ind 2 dimensions at all h the gibbs state is unique for almost all field configurations and in the random bond potts model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point the results are explained by the argument of imry and ma 1 the proofs involve the analysis of fluctuations of free energy differences which are shown using martingale techniques to be gaussian on the suitable scale

kms states and the chemical potential for disordered systems we extend the theory of the chemical potential associated to a compact separable gauge group to the case of disordered quantum systems this is done in the framework of operator algebras among the other results we show that the chemical potential does not depend on the disorder the situation of the n torus is treated in some detail indeed the chemical potential is intrinsically defined in terms of the direct integral decomposition of the connes radon nikodym cocycle associated to the normal extension of the kms state and its trasforms by the localized automorphisms of the observable algebra carrying the abelian charges of the model under consideration this description parallels the analogous one relative to the usual i e non disordered quantum models

regularity for double phase variational problems we prove sharp regularity theorems for minimisers of a class of variational integrals whose integrand switches between two different types of degenerate elliptic phases according to the zero set of a modulating coefficient a cdot the model case is given by the functional w mapsto int dw p a x dw q rm d x where q p and a cdot geqq 0

regularity results for a class of functionals with non standard growth we consider the integral functional under non standard growth assumptions that we call p x type namely we assume that a relevant model case being the functional under sharp assumptions on the continuous function p x 1 we prove regularity of minimizers energies exhibiting this growth appear in several models from mathematical physics

the thermodynamic limit for long range random systems long range spin systems with random interactions are considered a simple argument is presented showing that the thermodynamic limit of the free energy exists and depends neither on the specific random configuration nor on the sample shape provided there is no external field the argument is valid for both classical and quantum spin systems and can be applied to a spins randomly distributed on a lattice and interacting via dipolar interactions and b spin systems with potentials of the formj x 1 x 2 x 1 x 2 d where thej x 1 x 2 are independent random variables with mean zero d is the dimension and 1 2 the key to the proof is a multidimensional subadditive ergodic theorem as a corollary we show that for random ferromagnets the correlation length is a nonrandom quantity

nonlocal harnack inequalities abstract we state and prove a general harnack inequality for minimizers of nonlocal possibly degenerate integro differential operators whose model is the fractional p laplacian

on the parameterization of positive real sequences and ma parameter estimation an algorithm for moving average ma parameter estimation was proposed by stoica et al see ibid vol 48 p 1999 2012 2000 its key step covariance fitting is a semidefinite programming sdp problem with two convex constraints one reflecting the real positiveness of the desired covariance sequence and the other having a second order cone form we analyze two parameterizations of a positive real sequence and show that there is a one to one correspondence between them we also show that the dual of the covariance fitting problem has a significantly smaller number of variables and thus a much reduced computational complexity we discuss in detail the formulations that are best suited for the currently available semidefinite quadratic programming packages experimental results show that the execution times of the newly proposed algorithms scale well with the ma order which are therefore convenient for large order ma signals

optimization of two dimensional iir filters with nonseparable and separable denominator we present algorithms for the optimization of two dimensional 2 d infinite impulse response iir filters with separable or nonseparable denominator for least squares or chebyshev criteria the algorithms are iterative and each iteration consists of solving a semidefinite programming problem for least squares designs we adapt the gauss newton idea which outcomes to a convex approximation of the optimization criterion for chebyshev designs we adapt the iterative reweighted least squares irls algorithm in each iteration a least squares gauss newton step is performed while the weights are changed as in the basic irls algorithm the stability of the 2 d iir filters is ensured by keeping the denominator inside convex stability domains which are defined by linear matrix inequalities for the 2 d nonseparable case this is a new contribution based on the parameterization of 2 d polynomials that are positive on the unit bicircle in the experimental section 2 d iir filters with separable and nonseparable denominators are designed and compared we show that each type may be better than the other depending on the design specification we also give an example of filter that is clearly better than a recent very good design

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

calderon zygmund estimates for general elliptic operators with double phase abstract we derive calderon zygmund type estimates for the gradient of bounded distributional solutions to the problem div b x u d u p 2 d u a x d u q 2 d u div f p 2 f a x f q 2 f where 1 p q and 0 a c the coefficient b x z is supposed to be small bmo with respect to x and merely continuous in z

polynomial root radius optimization with affine constraints the root radius of a polynomial is the maximum of the moduli of its roots zeros we consider the following optimization problem minimize the root radius over monic polynomials of degree n with either real or complex coefficients subject to k linearly independent affine constraints on the coefficients we show that there always exists an optimal polynomial with at most k 1 inactive roots that is roots whose moduli are strictly less than the optimal root radius we illustrate our results using some examples arising in feedback control

type iii representations and modular spectral triples for the noncommutative torus abstract it is well known that for any irrational rotation number the noncommutative torus a must have representations such that the generated von neumann algebra a is of type iii therefore it could be of interest to exhibit and investigate such kind of representations together with the associated spectral triples whose twist of the dirac operator and the corresponding derivation arises from the tomita modular operator in the present paper we show that this program can be carried out at least when is a liouville number satisfying a faster approximation property by rationals in this case we exhibit several type i i and ii i 0 1 factor representations and modular spectral triples the method developed in the present paper can be generalised to ccr algebras based on a locally compact abelian group equipped with a symplectic form

optimal design of iir digital filters with robust stability using conic quadratic programming updates in this paper minimax design of infinite impulse response iir filters with prescribed stability margin is formulated as a conic quadratic programming cqp problem cqp is known as a class of well structured convex programming problems for which efficient interior point solvers are available by considering factorized denominators the proposed formulation incorporates a set of linear constraints that are sufficient and near necessary for the iir filter to have a prescribed stability margin a second order cone condition on the magnitude of each update that ensures the validity of a key linear approximation used in the design is also included in the formulation and eliminates a line search step collectively these features lead to improved designs relative to several established methods the paper then moves on to extend the proposed design methodology to quadrantally symmetric two dimensional 2 d digital filters simulation results for both one dimensional 1 d and 2 d cases are presented to illustrate the new design algorithms and demonstrate their performance in comparison with several existing methods

endpoint sobolev and bv continuity for maximal operators abstract in this paper we investigate some questions related to the continuity of maximal operators in w 1 1 and bv spaces complementing some well known boundedness results letting m be the one dimensional uncentered hardy littlewood maximal operator we prove that the map f m f is continuous from w 1 1 r to l 1 r in the discrete setting we prove that m b v z b v z is also continuous for the one dimensional fractional hardy littlewood maximal operator we prove by means of counterexamples that the corresponding continuity statements do not hold both in the continuous and discrete settings and for the centered and uncentered versions

convex optimization problems involving finite autocorrelation sequences we discuss convex optimization problems in which some of the variables are constrained to be finite autocorrelation sequences problems of this form arise in signal processing and communications and we describe applications in filter design and system identification autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density which results in a set of linear inequalities they can also be cast as linear matrix inequalities via the kalman yakubovich popov lemma the linear matrix inequality formulation is exact and results in convex optimization problems that can be solved using interior point methods for semidefinite programming however it has an important drawback to represent an autocorrelation sequence of length n it requires the introduction of a large number n n 1 2 of auxiliary variables this results in a high computational cost when general purpose semidefinite programming solvers are used we present a more efficient implementation based on duality and on interior point methods for convex problems with generalized linear inequalities

a weighted least squares method for the design of stable 1 d and 2 d iir digital filters we present a new approach to the least squares design of stable infinite impulse response iir digital filters the design is accomplished by using an iterative scheme in which the denominator polynomial obtained from the preceding iteration is treated as a part of the weighting function and each iteration is carried out by solving a standard quadratic programming problem that yields a stable rational function when the iteration converges a stable and truly least squares solution is obtained the method is then extended to address the least squares design of stable iir two dimensional 2 d filters examples are included to illustrate the proposed design techniques

regularity results for vectorial minimizers of a class of degenerate convex integrals abstract we establish the higher differentiability and the higher integrability for the gradient of vectorial minimizers of integral functionals with p q growth conditions we assume that the non homogeneous densities are uniformly convex and have a radial structure with respect to the gradient variable only at infinity the results are obtained under a possibly discontinuous dependence on the spatial variable of the integrand

higher integrability for minimizers of integral functionals with p q growth abstract we prove higher integrability for minimizers u r n of integral functionals f du a x u dx where f satisfies a non standard growth condition of p q type z p f z l 1 z q p

cartan subalgebras transverse measures and non type i plancherel formulae abstract two formulations are given of plancherel theory for locally compact second countable groups the first applies to arbitrary such groups and recovers the l 2 norm of suitable functions on the group from data associated to the central decomposition of the regular representation the second applies in particular to connected or discrete amenable groups and uses data derived from the irreducible representations appearing in a decomposition over a cartan subalgebra and connes ideas of transverse measures and functions in the recovery process non trivial examples are also given

design of optimal controllers for spatially invariant systems with finite communication speed we consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed we introduce a state space framework in which all spatially invariant systems with this property can be characterized after establishing the closure of such systems under linear fractional transformations we formulate the h 2 optimal control problem using the model matching framework we demonstrate that even though the optimal control problem is non convex with respect to some state space design parameters a variety of numerical optimization algorithms can be employed to relax the original problem thereby rendering suboptimal controllers in particular for the case in which every subsystem has scalar input disturbance scalar measurement and scalar actuation signal we investigate the application of the steiglitz mcbride gauss newton and newton iterative schemes to the optimal distributed controller design problem we apply this framework to examples previously considered in the literature to demonstrate that by designing structured controllers with infinite impulse response superior performance can be achieved compared to finite impulse response structured controllers of the same temporal degree

fixed order controller design for polytopic systems using lmis convex parameterization of fixed order robust stabilizing controllers for systems with polytopic uncertainty is represented as a linear matrix inequality lmi using the kalman yakubovich popov kyp lemma this parameterization is a convex inner approximation of the whole nonconvex set of stabilizing controllers and depends on the choice of a central polynomial it is shown that with an appropriate choice of the central polynomial the set of all stabilizing fixed order controllers that place the closed loop poles of a polytopic system in a disk centered on the real axis can be outbounded with some lmis these lmis can be used for robust pole placement of polytopic systems

stability of eigenvalues for variable exponent problems abstract in the framework of variable exponent sobolev spaces we prove that the variational eigenvalues defined by inf sup procedures of rayleigh ratios for the luxemburg norms are all stable under uniform convergence of the exponents

sharp regularity for functionals with p q growth we prove regularity theorems for minimizers of integral functionals of the calculus of variations f x du x dx with non standard growth conditions of p q type z p f x z l z q 1 p q in particular we find that a sufficient condition for minimizers to be regular is qp n n where the function f x z is holder continuous with respect to the x variable and x rn this condition is also sharp we include results in the setting of orlicz spaces moreover we treat certain relaxed functionals too finally we address a problem posed by marcellini in 43 showing a minimizer with an isolated singularity

multistage iir filter design using convex stability domains defined by positive realness in this paper we consider infinite impulse response iir filter design where both magnitude and phase are optimized using a weighted and sampled least squares criterion we propose a new convex stability domain defined by positive realness for ensuring the stability of the filter and adapt the steiglitz mcbride sm gauss newton gn and classical descent methods to the new stability domain we show how to describe the stability domain such that the description is suited to semidefinite programming and is implementable exactly in addition we prove that this domain contains the domain given by rouche spl acute s theorem finally we give experimental evidence that the best designs are usually obtained with a multistage algorithm where the three above methods are used in succession each one being initialized with the result of the previous and where the positive realness stability domain is used instead of that defined by rouche spl acute s theorem

existence of renormalized solutions to elliptic equation in musielak orlicz space abstract we prove existence of renormalized solutions to general nonlinear elliptic equation in musielak orlicz space avoiding growth restrictions namely we consider div a x u f l 1 on a lipschitz bounded domain in r n the growth of the monotone vector field a is controlled by a generalized nonhomogeneous and anisotropic n function m the approach does not require any particular type of growth condition of m or its conjugate m neither 2 nor 2 the condition we impose is log holder continuity of m which results in good approximation properties of the space the proof of the main results uses truncation ideas the young measures methods and monotonicity arguments

on the structure of kms states of disordered systems we study the set of kms states of spin systems with random interactions this is done in the framework of operator algebras by investigating connes and borchers invariants of w dynamical systems in the case of kms states exhibiting a property of invariance with respect to the spatial translations some interesting properties emerge naturally such a situation covers kms states obtained by infinite volume limits of finite volume gibbs states that is the quenched disorder this analysis can be considered as a step towards fully understanding the very complicated structure of the set of temperature states of quantum spin glasses and its connection with the breakdown of the symmetry for replicas

harnack inequalities for double phase functionals we prove a harnack inequality for minimisers of a class of non autonomous functionals with non standard growth conditions they are characterised by the fact that their energy density switches between two types of different degenerate phases

pcls iir digital filters with simultaneous frequency response magnitude and group delay specifications this paper presents the peak constrained least squares pcls approach to designing iir digital filters pcls iir digital filters that meet simultaneous specifications on the frequency response magnitude and the group delay are introduced as a point of reference we consider the iir digital filter design problem that appears in deczky s 1972 classic paper and in the popular textbook by oppenheim and schafer 1989 in addition the same design problem appears in the iir filter design chapter by higgins and munson 1993 in the handbook for digital signal processing by using our new algorithm with simultaneous optimization of the frequency response magnitude and the group delay we obtain a dramatic improvement in the solution of this classic iir digital filter design problem starting from the same filter structure and the same specifications for the frequency response magnitude as in the works of deczky oppenheim and schafer and higgins and munson we are able to reduce the group delay ripple by a factor of 35 in another design problem that originated in deczky s work we use pcls optimization to reduce the group delay ripple by a factor of 40 at the same time we reduce the stopband energy by 6 db without sacrificing any other performance measure the group delay ripple in this iir digital filter example is reduced to only spl plusmn 0 002 samples

holder continuity for nonlinear elliptic problem in musielak orlicz sobolev space abstract under appropriate assumptions on the n function the de giorgi process is presented by the tools recently developed in musielak orlicz sobolev space to prove the holder continuity of fully nonlinear elliptic problems as the applications the holder continuity of the minimizers for a class of the energy functionals in musielak orlicz sobolev spaces is proved and furthermore the local holder continuity of the weak solutions for a class of fully nonlinear elliptic equations is provided

regularity for double phase problems under additional integrability assumptions abstract we study the regularity of quasi minimizers or minimizers of functionals of double phase type in recent years baroni colombo and mingione have investigated regularity theory for bounded minimizers in baroni et al 2015 2018 colombo and mingione 2015 in this paper we assume the minimizers only belong to l space

regularity for minimizers of double phase functionals with mild transition and regular coefficients abstract we prove sharp regularity results for minimizers of the functional p w b x w d w p a x d w p log e d w d x with w w 1 1 p 1 a l a 0 and 0 b l p is a double phase functional with mild transition between d u p and d u p log e d u first under suitable conditions on the moduli of continuity of a and b we prove that local minimizers are of class c 0 for every 0 1 then that they are of class c 1 for some 0 provided the functions a and b are holder continuous

scalar minimizers with fractal singular sets lack of regularity of local minimizers for convex functionals with non standard growth conditions is considered it is shown that for every 0 there exists a function ac such that the functional admits a local minimizer uw1 p whose set of non lebesgue points is a closed set with dim n p and where 1 p n n q

minimax design of iir digital filters using a sequential constrained least squares method the minimax design of infinite impulse response iir digital filters is a nonconvex optimization problem and thus has many local minima it is shown in this correspondence that a sequential constrained least squares scls method has a higher possibility of obtaining better solutions than a direct minimization method when applied to the nonconvex minimax design of iir filters we combine the scls method with a steiglitz mcbride sm strategy resulting in a practical design procedure the positive realness stability condition proposed by dumitrescu and niemisto is reformulated as linear inequality constraints and then incorporated in the design procedure simulation examples and comparisons with several existing methods demonstrate the effectiveness of the procedure and good performances of the designed filters

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

existence and multiplicity results for double phase problem abstract by variational method we obtain various existence and multiplicity results for the following double phase problem div u p 2 u a x u q 2 u f x u in u 0 on in particular we find a sign changing ground state solution some properties of double phase operator are also obtained

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

variable exponent functionals in image restoration abstract we study a functional with variable exponent 1 p x 2 which provides a model for image denoising and restoration here p x is defined by the gradient information in the observed image the diffusion derived from the proposed model is between total variation based regularization and gaussian smoothing the diffusion speed of the corresponding heat equation is tuned by the variable exponent p x the minimization problem and its associated flow in a weakened formulation are discussed the existence uniqueness stability and long time behavior of the proposed model are established in the variable exponent functional space w 1 p x experimental results illustrate the effectiveness of the model in image restoration

minimax phase error design of iir digital filters with prescribed magnitude and phase responses infinite impulse response iir digital filters with prescribed magnitude and phase responses have been used in many applications to approximate the prescribed magnitude and phase responses we propose a new approach to the design of general iir filters by minimizing the maximum phase error subject to a prescribed or simultaneously minimized maximum magnitude error where the phase error and magnitude error are controlled by two elliptic constraints respectively with major and minor axes along the desired frequency response the sequential constrained least squares method and levy sanathanan koerner strategy are used to convert the nonconvex constraints into convex ones resulting in a series of convex optimization subproblems design examples and comparisons with recent methods demonstrate the flexibility and effectiveness of the proposed methods

regularity results for a class of obstacle problems with nonstandard growth abstract we consider the obstacle problem related to the following energy with nonstandard growth d u p x log e d u d x we investigate the regularity properties of solutions to the obstacle problems along with a suitable assumptions on the variable exponent p and the obstacle

global lorentz estimates for nonuniformly nonlinear elliptic equations via fractional maximal operators abstract this article is a contribution to the study of regularity theory for nonlinear elliptic equations the aim of this article is to establish some global estimates for nonuniformly elliptic equations in divergence form as div u p 2 u a x u q 2 u div f p 2 f a x f q 2 f which arises from double phase functional problems in particular the main results provide the regularity estimates for the distributional solutions in terms of maximal and fractional maximal operators this work extends that of colombo and mingione 2016 23 and byun and oh 2017 9 by dealing with the global estimates in lorentz spaces it also extends our recent result tran and nguyen 2020 66 concerning new estimates of divergence elliptic equations using cutoff fractional maximal operators for future research the approach developed in this article will allow global estimates of distributional solutions to nonuniformly nonlinear elliptic equations to be obtained in the framework of other spaces

partial regularity for general systems of double phase type with continuous coefficients abstract we consider elliptic systems of double phase problems which satisfy a general structure with continuous coefficients and prove that weak solutions of such systems are holder continuous for any holder exponent 0 1 except for a measure zero set

bounded minimisers of double phase variational integrals bounded minimisers of the functional w mapsto int dw p a x dw q rm d x where 0 leqq a cdot in c 0 alpha and 1 p q are c 1 beta regular provided the sharp bound q leqq p alpha holds

multiple solutions for a class of double phase problem without the ambrosetti rabinowitz conditions abstract in the present paper in view of the variational approach we consider the existence and multiplicity of weak solutions for a class of the double phase problem div u p 2 u a x u q 2 u f x u in u 0 on where n 2 and 1 p q n firstly by the fountain and dual theorem with cerami condition we obtain some existence of infinitely many solutions for the above problem under some weaker assumptions on f secondly we prove that this problem has at least one nontrivial solution for any parameter 0 small enough and also that the solution blows up in the sobolev norm as 0 finally by imposing additional assumptions on f we establish the existence of infinitely many solutions by using krasnoselskii s genus theory for the above equation

an improved bias compensation approach for errors in variables model identification parametric estimation of the dynamic errors in variables models is considered in this paper in particular a bias compensation approach is examined in a generalized framework sufficient conditions for uniqueness of the identified model are presented subsequently a statistical accuracy analysis of the estimation algorithm is carried out the asymptotic covariance matrix of the system parameter estimates depends on a user chosen filter and a certain weighting matrix it is shown how these can be tuned to boost the estimation performance the numerical simulation results suggest that the covariance matrix of the estimated parameter vector is very close to the cramer rao lower bound for the estimation problem

existence and uniqueness of elliptic systems with double phase operators and convection terms abstract in this paper we study quasilinear elliptic systems driven by so called double phase operators and nonlinear right hand sides depending on the gradients of the solutions based on the surjectivity result for pseudomonotone operators we prove the existence of at least one weak solution of such systems furthermore under some additional conditions on the data the uniqueness of weak solutions is shown

least squares design of iir filters with prescribed magnitude and phase responses and a pole radius constraint this paper presents a method for the frequency domain design of infinite impulse response iir digital filters the proposed method designs filters approximating prescribed magnitude and phase responses iir filters of this kind can have approximately linear phase responses in their passbands or they can equalize magnitude and phase responses of given systems in many cases these filters can be implemented with less memory and with fewer computations per output sample than equivalent finite impulse response fir digital filters an important feature of the proposed method is the possibility to specify a maximum radius for the poles of the designed rational transfer function consequently stability can be guaranteed and undesired effects of implementations using fixed point arithmetic can be alleviated by restricting the poles to keep a prescribed distance from the unit circle this is achieved by applying rouche s theorem in the proposed design algorithm we motivate the use of iir filters with an unequal number of poles and zeros outside the origin of the complex plane in order to satisfy simultaneous specifications on magnitude and phase responses it is advantageous to use iir filters with only a few poles outside the origin of the z plane and an arbitrary number of zeros filters of this type are a compromise between iir filters with optimum magnitude responses and phase approximating fir filters we use design examples to compare filters designed by the proposed method to those obtained by other methods in addition we compare the proposed general iir filters with other popular more specialized structures such as fir filters and cascaded systems consisting of frequency selective iir filters and phase equalizing allpass filters

iterative reweighted minimax phase error designs of iir digital filters with nearly linear phases linear phase is an important characteristic of digital filters in many signal processing applications in this paper two iterative reweighted minimax phase error algorithms are proposed to design nearly linear phase infinite impulse response iir digital filters with prescribed or simultaneously minimized magnitude errors and preset transition band gain in each iteration of the algorithms a weighted minimax phase error problem with a fixed weight function is firstly solved using a modified gauss newton method with a variable step length and the weight function of the phase error is then updated using the square root of a modified envelope of the group delay error of the filter with the proposed methods both very small phase error and group delay error have been obtained while meeting the requirements on the passband and stopband magnitude errors and the transition band gain design examples demonstrate the effectiveness of the proposed methods and the excellent performance of the designed filters

improved design method for nearly linear phase iir filters using constrained optimization a new optimization method for the design of nearly linear phase iir digital filters that satisfy prescribed specifications is proposed the group delay deviation is minimized under the constraint that the passband ripple and stopband attenuation are within the prescribed specifications and either a prescribed or an optimized group delay can be achieved by representing the filter in terms of a cascade of second order sections a non restrictive stability constraint characterized by a set of linear inequality constraints can be incorporated in the optimization algorithm an additional feature of the method which is very useful in certain applications is that it provides the capability of constraining the maximum gain in transition bands to be below a prescribed level experimental results show that filters designed using the proposed method have much lower group delay deviation for the same passband ripple and stopband attenuation when compared with corresponding filters designed with several state of the art competing methods

regularity for multi phase variational problems abstract we prove c 1 regularity for local minimizers of the multi phase energy w d w p a x d w q b x d w s d x under sharp assumptions relating the couples p q and p s to the holder exponents of the modulating coefficients a and b respectively

a wise method for designing iir filters the problem of designing optimal digital iir filters with frequency responses approximating arbitrarily chosen complex functions is considered the real valued coefficients of the filter s transfer function are obtained by numerical minimization of carefully formulated cost which is referred here to as the weighted integral of the squared error wise criterion the wise criterion linearly combines the wls criterion that is used in the weighted least squares approach toward filter design and some time domain components the wls part of wise enforces the quality of the frequency response of the designed filter while the time domain part of the wise criterion restricts the positions of the filter s poles to the interior of an origin centred circle with arbitrary radius this allows one not only to achieve stability of the filter but also to maintain some safety margins a great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off the shelf optimization procedures the power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature

double phase image restoration abstract in this paper we explore the potential of the double phase functional in an image processing context to this end we study minimizers of the double phase energy for functions with bounded variation and show that this energy can be obtained by convergence or relaxation of regularized functionals a central tool is a capped fractional maximal function of the derivative of bv functions

harnack s inequality for quasiminimizers with nonstandard growth conditions we prove harnack inequalities for quasiminimizers of the variable exponent dirichlet energy integral by employing the de giorgi method