multiplier free iir filter realization using periodically time varying state space structure i structure and design a multiplier free realization for iir filters is proposed a given target iir filter is implemented in cascade or parallel form of biquad units each biquad unit is realized with a periodically time varying ptv state space system the system uses a higher order ptv state space ptv ss structure operating at an elevated signal rate to realize each biquad the coefficients of the ptv ss structure used in the realization are restricted to a few power of two values therefore such a structure can be implemented without any hardware multiplier a brief analysis of precision and round off error for the realization is presented examples show that the frequency response of the proposed realization matches very well with that of the target filter

peak error constrained sparse fir filter design using iterative socp in this paper a novel algorithm is proposed to design sparse fir filters it is known that this design problem is highly nonconvex due to the existence of norm of a filter coefficient vector in its objective function to tackle this difficulty an iterative procedure is developed to search a potential sparsity pattern which is then used to compute the final solution by solving a convex optimization problem in each iterative step the original sparse filter design problem is successively transformed to a simpler subproblem it can be proved that under a weak condition globally optimal solutions of these subproblems can be attained by solving their dual problems in this case the overall iterative procedure converges to a locally optimal solution of the original design problem the design procedure described above can be repeated for several times to further improve the sparsity of design results the output of the previous stage can be used as the initial point of the subsequent design the performance of the proposed algorithm is evaluated by two sets of design examples and compared to other sparse fir filter design algorithms

new initialization methods for discrete coefficient fir filter design with coefficient scaling and the use of scale factor in the design process the initialization of filter coefficients in discrete coefficient finite impulse response fir filter design with coefficient scaling using coefficient value assignment based optimization techniques is considered a common weakness of existing initialization measures a total square error tse measure and a maximum error me measure is described new tse and me measures that overcome the weakness are introduced as opposed to the current knowledge it is revealed that tse and me measures do not necessarily provide different initial coefficient set information and that the initial coefficient set information by the me measure is not unique in general on a parallel track the treatment of coefficient scaling in the optimization process is considered the closed form expression of the objective function normalized peak ripple magnitude nprm which was defined implicitly in the literature is given in contrast to existing methods the computation of nprm accordingly does not require a scale factor parameter independent of filter coefficients although coefficient scaling persists then tse and me measures become practically equivalent although in general they indicate different initial scale factors since an explicit scale factor parameter is no longer needed

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

closed form solutions for a generalized benjamin bona mahony burgers equation with higher order nonlinearity we obtain closed form solutions for a generalized benjamin bona mahony burgers gbbmb equation with higher order nonlinearity which belong to a class of so called nonlinear pseudo parabolic or type sobolev equations the generalized tanh coth method is used here with the aid of mathematica periodic and soliton solutions are formally derived finally some conclusions are given

semisystolic incremental realization of fir digital filters using ternary arithmetic a fully incremental realization of finite impulse response fir filters is presented in which ternary incremental representations are used for all the signals in the structure and the impulse response delta modulation dm is used for this purpose allowing a considerable simplification of the arithmetic involved in the filtering operations simulation showed that the proposed dm adder has lower mean square error mse and reduced processing delay with respect to existing dm adders while demonstrating the feasibility of the proposed modular incremental realization for fir filters

a class of high precision multiplier free fir filter realizations with periodically time varying coefficients proposes a class of high precision multiplier free realizations for fir filters these realizations use upsampling and downsampling in conjunction with a periodically time varying system to achieve time invariant multiplier free fir filter operation nonbinary encoding schemes are used for obtaining the filter coefficients which are periodically time varying ptv i e they vary in a periodic fashion each target filter coefficient is directly mapped into a set of ptv coefficients so that the realizations are easy to obtain the values of the ptv coefficients are restricted to either the ternary set

decomposition of fir digital filters for realization via the cascade connection of subfilters a method is presented for decomposing even order linear phase fir filters with distinct roots into the cascade connection of second and fourth order subfilters the technique consists of of finding roots of the z domain filter transfer function by searching a finite region in the complex z plane due to symmetry in the impulse response only the perimeter the real axis and boundary and interior of the upper half of the unit circle need to be searched for real and complex values of roots from which the impulse response coefficients of the corresponding subfilters can be directly determined the root finding algorithm tests for existence of a root at each interval in a finite grid and then utilizes the newton raphson method to refine the final estimate of each root value in the two dimensional 2 d search the cauchy riemann relations are exploited to reduce computations and speed convergence this method has been tested on fir filters with orders ranging to over 120 and has proven effective in decomposing filters to the cascade realization with identical frequency response characteristics an example is presented that illustrates the use of this technique

on a solution strategy for energy based mesh optimization in finite hyperelastostatics the objective of this work is the development of a numerical solution strategy for energy based mesh optimization in finite hyperelastostatics in finite element computations that rely on the principle of minimum potential energy the variational principle itself provides the basis for r adaptive methods the numerical solution can be improved by further minimizing the discrete potential energy with respect to the material node point positions in this paper we regard the mesh optimization as a nonlinear minimization problem with equality and inequality constraints the equality constraints correspond to the spatial equilibrium condition whereas the inequality constraints are given by the natural restriction that material elements with a negative volume jacobian are inadmissible based on this interpretation we develop a stable numerical solution strategy in which two approaches of nonlinear programming are combined applying a barrier method the minimization problem is transformed into a sequence of problems without inequality constraints each problem of the sequence is solved by means of a newton scheme that operates on the constrained surface given by the spatial equilibrium condition

roundoff noise reduction in cascade realizations of fir digital filters this correspondence presents the results of a numerical analysis of roundoff noise effects in cascade realizations or fir filters minimum noise realizations were designed through an exhaustive search over all possible subfilter orderings although it was found that computation time was impractical for filters with more than approximately ten subfilters the hypothesis that arranging filters in order of decreasing bandwidth reduces roundoff noise was tested and found to be ineffective for fir filters simulated annealing was tested and found to be an effective technique for reducing roundoff noise in cascade connection realizations of fir digital filters the simulated annealing algorithm was adapted to this problem and was found to yield subfilter orderings with roundoff noise gain very near the minimum achievable results are presented that illustrate these findings

on a kdv equation with higher order nonlinearity traveling wave solutions abstract in this work the improved tanh coth method is used to obtain wave solutions to a korteweg de vries kdv equation with higher order nonlinearity from which the standard kdv and the modified korteweg de vries mkdv equations with variable coefficients can be derived as particular cases however the model studied here include other important equations with applications in several fields of physical and nonlinear sciences periodic and soliton solutions are formally derived

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

an integrated approach to shape optimization and mesh adaptivity based on material residual forces abstract this contribution is concerned with the coupling of finite element based shape optimization to methods of mesh adaptivity therein the nodal points of a finite element mesh serve as design variables in an optimization problem that aims to minimize a cost functional with respect to different constraints in order to avoid the occurrence of oscillating boundaries in the optimal design trials we generate the respective design updates through solving a series of fictitious boundary value problems on an updated lagrangian configuration the design update process is accompanied by adaptive mesh refinement to obtain more accurate results for the structural analysis and the design sensitivity analysis for the mesh adaptation process we consider r adaptive node relocation h adaptive mesh refinement and a combination of both approaches in each case the derivations rest upon the notion of material residual forces induced by finite element discretization and the coupling of shape optimization and mesh adaptivity is of intermittent type i e mesh adaptivity is invoked once a certain number of design updates has been generated we examine the benefits of the proposed method on the basis of some numerical examples in comparison to the same shape optimization method not involving adaptive mesh refinement where we evaluate the corresponding numerical costs the gain in accuracy and the effects on the optimal shapes being obtained

a generalized lattice filter for finite wordlength implementation with reduced number of multipliers the excellent finite wordlength fwl property of lattice digital filters is well known the four multiplier normalized lattice with signal power at all delay elements normalized to unity has particular advantage in its overflow property however when used to implement an nth order digital filter the normalized lattice implementation requires 5n 1 multipliers there exists another lattice structure with excellent fwl property called the injected numerator lattice structure in this paper we combine the injected numerator lattice and tapped numerator lattice to form a new hybrid lattice structure which is not only canonic in the number of multipliers resulting in a significant reduction in overall implementation cost but also exhibits much better fwl properties than the normalized lattice structure an improved peakedness measure is also introduced for application where the input signal has a strong time varying sinusoidal component the new structure requires a few additional adders it can be used to implement any causal and stable z transform transfer function two numerical examples are presented to demonstrate the performance of the proposed structure

optimum binary windows for discrete fourier transforms a class of windows called binary windows for the frequency domain implementation of the discrete fourier transform is proposed while the conventional time domain windowing requires n 2 stored values of the data window and n multiplications the binary windows do not require multiplications or stored constants rather they are replaced by shift and add operations typical hardware structures are presented for efficient implementation of the binary windows

lll algorithm and the optimal finite wordlength fir design in practical finite impulse response fir digital filter applications it is often necessary to represent the filter coefficients with a finite number of bits the finite wordlength restriction increases the filter deviation this increase can be reduced substantially if the optimal finite wordlength coefficients are used the time needed to compute these coefficients is greatly reduced with the help of a lower bound on the deviation increase derivation of an improved lower bound that uses the well known lll algorithm is presented in this correspondence

reduction of symmetric complex filters due to their linear phase property symmetric filters are an interesting class of finite impulse response fir filters moreover symmetric fir filters allow an efficient implementation in this paper we extend the classical definition of hermitian symmetry to a more general symmetry that is also applicable to complex filters this symmetry is called generalized hermitian symmetry we show the usefulness of this definition as it allows for a unified treatment of even and odd length filters central in this paper is a theorem on the reduction of generalized hermitian symmetric filters to hermitian symmetric filters both with finite precision coefficients a constructive proof of this theorem is presented and an associated procedure for reducing generalized hermitian symmetric filters is derived two of the examples show the application of the reduction procedure and the achieved savings on arithmetic costs finally all three examples show that a special instance of the generalized hermitian symmetric filters with finite precision coefficients may have lower arithmetic costs than the hermitian symmetric filter from which it is derived

improved filter sharpening we propose a natural extension to kaiser hamming 1977 filter sharpening methods to allow for a piecewise linear desired amplitude change function acf the primary advantages of the proposed acf over piecewise constant acfs is that we obtain better control of selective improvement or degradation in either the passband or stopband or both and we are not restricted to applying our methods to filters with piecewise constant pass and stopbands since linear segments of slope 1 can be used to retain existing filter performance in either passband or stopband the proposed acf approximating polynomial ap is easy to compute may be constrained to have simple or integer coefficients and may be expressed as the ap of kaiser and hamming plus a correction polynomial we also provide applications for motivation

a variational r adaption and shape optimization method for finite deformation elasticity this paper is concerned with the formulation of a variational r adaption method for finite deformation elastostatic problems the distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution the optimal mesh and in problems of shape optimization the equilibrium shapes of the system this is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes we derive general expressions for the configuration forces for isoparametric elements and nonlinear possibly anisotropic materials under general loading we illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications including the problem of a semi infinite crack in linear and nonlinear elastic bodies and the optimization of the shape of elastic inclusions

a computational methodology for shape optimization of structures in frictionless contact this paper presents a computational methodology for shape optimization of structures in frictionless contact which provides a basis for developing user friendly and efficient shape optimization software for evaluation it has been implemented as a subsystem of a general finite element software the overall design and main principles of operation of this software are outlined the parts connected to shape optimization are described in more detail the key building blocks are analytic sensitivity analysis an adaptive finite element method an accurate contact solver and a sequential convex programing optimization algorithm results for three model application examples are presented in which the contact pressure and the effective stress are optimized

a posteriori finite element bounds for linear functional outputs of elliptic partial differential equations we present a domain decomposition finite element technique for efficiently generating lower and upper bounds to outputs which are linear functionals of the solutions to symmetric or nonsymmetric second order coercive linear partial differential equations in two space dimensions the method is based upon the construction of an augmented lagrangian in which the objective is a quadratic energy reformulation of the desired output and the constraints are the finite element equilibrium equations and intersubdomain continuity requirements the bounds on the output for a suitably fine truth mesh discretization are then derived by appealing to a dual max min relaxation evaluated for optimally chosen adjoint and hybrid flux candidate lagrange multipliers generated by a k element coarser working mesh approximation independent of the form of the original partial differential equation the computation on the truth mesh is reduced to k decoupled subdomain local symmetric neumann problems the technique is illustrated for the convection diffusion and linear elasticity equations

noise reduction in recursive digital filters using high order error feedback the problem of solving the optimal minimum noise error feedback coefficients for recursive digital filters is addressed in the general high order case it is shown that when minimum noise variance at the filter output is required the optimization problem leads to set of familiar wiener hopf or yule walker equations demonstrating that the optimal error feedback can be interpreted as a special case of wiener filtering as an alternative to the optimal solution the formulas for suboptimal error feedback with symmetric or antisymmetric coefficients are derived in addition the design of error feedback using power of two coefficients is discussed the efficiency of high order error feedback is examined by test implementations of the set of standard filters it is concluded that error feedback is a very powerful and versatile method for cutting down the quantization noise in any classical infinite impulse response iir filter implemented as a cascade of second order direct form sections the high order schemes are attractive for use with high order direct form sections

shape optimization with p adaptivity the p method of analysis when used with shape optimization has certain advantages over the h method the method of h adaptivity results in fine meshes with small elements in areas of stress concentration the presence of these small elements prevents the shape from changing significantly during optimization due to mesh distortion the p adaptive method uses relatively large sized elements and adaptivity is achieved by increasing the polynomial order of the shape functions rather than by introducing small elements as in the h method thus the p adaptive method allows for greater shape changes without sacrificing the accuracy of the analysis a methodology is developed in this paper to integrate p adaptive analysis with shape optimization for general velocity fields the key contributions lie in an easily implementable shape update strategy and an adaptive scheme to locally increase the polynomial order based on error indicators numerical results show that significant shape change is achievable prior to serious mesh distortion in addition need for an h p adaptive strategy rather than a pure p adaptive strategy is also highlighted

shape sensitivity analysis in linear elastic fracture mechanics shape sensitivity analysis of an elastic solid in equilibrium with a known load system applied over its boundary is presented in this work the domain and boundary integral expressions of the first and second order shape derivatives of the total potential energy are established by using an arbitrary change of the domain characterized by a velocity field defined over the initial body configuration in these expressions we recognize free divergence tensors that are denoted in this paper as energy shape change tensors next shape sensitivity analysis is applied to cracked bodies for that purpose a suitable velocity distribution field is adopted to simulate the crack advance of a unit length in a two dimensional body finally the corresponding domain and the equivalent path independent integral expressions of the first and second order potential energy release rate of fracture mechanics are also derived

design of discrete coefficient fir filters on loosely connected parallel machines this paper presents a new branch and bound mixed integer linear programming based algorithm for designing discrete coefficient finite impulse response fir filters using a cluster of workstations as the computation platform the discrete coefficient space considered is the sum of signed power of two space but the technique is also applicable to other discrete coefficient spaces the key issue determining the success of the algorithm is the ability to partition the original problem into several independent parts that can be distributed to a cluster of machines for solution the master slave model is adopted for the control of the machines test run results showed that super linear speedup i e the speedup factor is more than the number of machines running in parallel may be achieved

the gradient of the finite element variational indicator with respect to nodal and applications in fracture mechanics and mesh optimization we derive a closed form expression for the change in the variational indicator of a finite element mesh with respect to perturbations in nodal point co ordinates the expression is evaluated very effectively from standard finite element data obtained in one solution and may be easily programmed as part of a general finite element code we present the derivation for two and three dimensional isoparametric elements used in linear and nonlincar elasticity the expression has practical applications in the computation of stress intensity factors in fracture mechanics and in the determination of the optimal mesh with a given element node connectivity we demonstrate both applications by accurately determining the stress intensity factor of a mode i crack using a finite element mesh which was improved using mesh optimization

goal oriented error estimation and adaptivity for the finite element method abstract in this paper we study a new approach in a posteriori error estimation in which the numerical error of finite element approximations is estimated in terms of quantities of interest rather than the classical energy norm these so called quantities of interest are characterized by linear functionals on the space of functions to where the solution belongs we present here the theory with respect to a class of elliptic boundary value problems and in particular show how to obtain accurate estimates as well as upper and lower bounds on the error we also study the new concept of goal oriented adaptivity which embodies mesh adaptation procedures designed to control error in specific quantities numerical experiments confirm that such procedures greatly accelerate the attainment of local features of the solution to preset accuracies as compared to traditional adaptive schemes based on energy norm error estimates

derivation of a new analytical solution for a general two dimensional finite part integral applicable in fracture mechanics an exact expression is derived for the general finite part integral over an inclined ellipticaldomain r denotes the distance of a point in to the singular point is a general function of the cartesian co ordinates x0 y0 the boundary of the region represents the equation z x0 y0 o these integrals appear during the numerical solution of plane crack problems in three dimensional elasticity where they are the dominant part of a hypersingular integral equation the availability of exact expressions for the integrals with arbitrary integers i and j will increase the accuracy of the numerical results and simultaneously lead to quicker numerical results the considered finite part integral can be expressed in closed form as function of complete elliptical integrals or gauss hypergeometric functions respectively formuias for special cases and some i j values and their numerical verification are given in appendices ii and iii

design of cascade form fir filters with discrete valued coefficients the authors show that by cascading two direct form fir filters each with coefficients that are the sum or difference of two power of two terms it is possible to achieve very small peak ripple an iterative equalization strategy is used in the design of the cascaded filter the success of the method depends on the initial prototype filter being used two equally effective methods are presented for selecting the prototype filter each yields a final design with good roundoff noise property

a general methodology for structural shape optimization problems using automatic adaptive remeshing this methodology is based on the use of the adaptive mesh refinement techniques in the context of 2d shape optimization problems a technique for the parametrization of the optimization problem using b splines to define the boundary is first presented then mesh generation using the advancing frontal method the error estimator and the mesh refinement criterion are studied in the context of shape optimization problems in particular the analytical sensitivity analysis of the different items ruling the problem b splines finite element mesh structural behaviour and error estimator is studied in detail

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

hypersingular residuals a new approach for error estimation in the boundary element method summary this paper presents a new approach for a posteriori pointwise error estimation in the boundary element method the estimator relies upon evaluation of the residual of hypersingular integral equations and is therefore intrinsic to the boundary integral equation approach a methodology is developed for approximating the error on the boundary as well as in the interior of the domain extensive computational experiments have been performed for the two dimensional laplace equation and the numerical results indicate that the error estimates successfully track the form of the exact error curve moreover a reasonable estimate of the magnitude of the actual error is also predicted

on efficient solutions to the continuous sensitivity equation using automatic differentiation shape sensitivity analysis is a tool that provides quantitative information about the influence of shape parameter changes on the solution of a partial differential equation pde these shape sensitivities are described by a continuous sensitivity equation cse automatic differentiation ad can be used to perform this sensitivity analysis without writing any additional code to solve the sensitivity equation the approximate solution of the pde uses a spatial discretization mesh that often depends on the shape parameters therefore the straightforward application of ad introduces derivatives of the mesh there are two drawbacks to this approach first extra computational effort especially memory is used in these calculations due to mesh sensitivities second this mesh sensitivity information needs to be computed in order to obtain accurate results in this work we provide a methodology that avoids mesh sensitivities and their drawbacks by defining a modified pde on a fixed domain i e independent of the shape parameter such that ad provides the desired approximation of the cse using two examples we demonstrate significant improvement in the computational effort both in terms of floating point operations and memory requirements we explain how these code modifications can be applied to a wide variety of practical problems with minimal changes to the original code these changes are negligible when compared to the complexity of writing a separate solver for the sensitivity equation

state space newton s method for topology optimization abstract we introduce a new algorithm for solving certain classes of topology optimization problems which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space the computational complexity of newton s direction finding subproblem in the algorithm is comparable with that of finding the steepest descent direction in the traditional first order nested reduced space algorithms for topology optimization that is the space reduction is computationally inexpensive and more importantly it does not ruin the sparsity of the full space system of optimality conditions the fast local convergence of the algorithm allows one to efficiently solve a sequence of optimization problems for varying parameters numerical continuation this can be utilized for eliminating the errors introduced by the approximate enforcement of the boundary conditions or 0 1 type constraints on the design field through penalties in many topology optimization approaches we test the algorithm on the benchmark problems of dissipated power minimization for stokes flows and in all cases the algorithm outperforms the traditional first order reduced space nested approaches by a factor varying from two to almost twenty in terms of the number of iterations while attaining an almost unprecedented accuracy in solving the discretized topology optimization problem finally we present a few extensions to the algorithm one involving computations on adaptively refined meshes and another related to solving topology optimization problems for non newtonian fluids

design and analysis of recursive periodically time varying digital filters with highly quantized coefficients a design for recursive filters with coefficients epsilon 1 0 1 that can change at each filter update is introduced this flexibility of allowing the multipliers to be functions of time can be used to offset the reduction in degrees of freedom when such quantization is used this result will be especially useful in filtering applications in which a controllable or adaptive filter is required and high speed multipliers are not available a general transition matrix state variable formulation similar to floquet theory for differential equations is developed that can be used to design iir infinite impulse response filters characterized by a periodically time varying feedback matrix by defining a time varying similarity transformation and introducing circulant feedback matrices a significant simplification of the highly quantized time varying state recursion equation is realized this leads to the enumeration of the filter transfer function and to a simple eigenvalue structure that facilitates the design of filters with desired pole locations these analytical results are verified in simulations of lowpass and bandpass filter designs

a posteriori estimation and adaptive control of the pollution error in the h version of the finite element method abstract we studied the pollution error in the h version of the finite element method and its effect on the quality of the local error indicators resp the quality of the derivatives recovered by local postprocessing in the interior of the mesh here we show that it is possible to construct a posteriori estimates of the pollution error in a patch of elements by employing the local error indicators over the entire mesh we also give an adaptive algorithm for the local control of the pollution error in a patch of elements of interest

a discrete filled function method for the design of fir filters with signed powers of two coefficients in this paper we consider the optimal design of finite impulse response fir filters with coefficients expressed as sums of signed powers of two spt terms where the normalized peak ripple npr is taken as the performance measure this problem is formulated as a mixed integer programming problem based on a transformation between two different integer spaces and the computation of the optimal scaling factor for a given set of coefficients this mixed integer programming problem is transformed into an equivalent integer programming problem then an efficient algorithm based on a discrete filled function is developed for solving this equivalent problem for illustration some numerical examples are solved

optimal design of finite precision fir filters using linear programming with reduced constraints an algorithm for the design of optimal one dimensional 1 d and two dimensional 2 d fir filters over a discrete coefficient space is proposed the algorithm is based on the observation that the equiripple frequencies of a subproblem sp in the branch and bound bab algorithm are closely related to those of neighboring sps by using the relationship among the sps the proposed algorithm reduces the number of constraints required for solving each sp thus the overall computational load for the design of fir filters with discrete coefficients is significantly alleviated compared with the conventional bab algorithm

design and multiplier less implementation of a class of two channel pr fir filterbanks and wavelets with low system delay a new method for designing two channel pr fir filterbanks with low system delay is proposed it is based on the generalization of the structure previously proposed by phoong et al 1995 such structurally pr filterbanks are parameterized by two functions spl beta z and spl alpha z that can be chosen as linear phase fir or allpass functions to construct fir iir filterbanks with good frequency characteristics the case of using identical spl beta z and spl alpha z was considered by phoong et al with the delay parameter m chosen as 2n 1 in this paper the more general ease of using different nonlinear phase fir functions for spl beta z and spl alpha z is studied as the linear phase constraint is relaxed the lengths of spl beta z and spl alpha z are no longer restricted by the delay parameters of the filterbanks hence higher stopband attenuation can still be achieved at low system delay the design of the proposed low delay filterbanks is formulated as a complex polynomial approximation problem which can be solved by the remez exchange algorithm or analytic formula with very low complexity in addition the orders and delay parameters can be estimated from the given filter specifications using a simple empirical formula therefore low delay two channel pr filterbanks with flexible stopband attenuation and cutoff frequencies can be designed using existing filter design algorithms the generalization of the present approach to the design of a class of wavelet bases associated with these low delay filterbanks and its multiplier less implementation using the sum of powers of two coefficients are also studied

complexity reduction of digital filters using shift inclusive differential coefficients we present a graph theoretical methodology that reduces the implementation complexity of the multiplication of a constant vector and a scalar the complexity of implementation is defined as the required amount of computations like additions the proposed approach is called minimally redundant parallel mrp optimization and is mainly presented in a finite impulse response fir filtering framework to obtain a low complexity multiplierless implementation the key idea is to expand the design space using shift inclusive differential coefficients sidcs together with computation reordering using a graph theoretic approach to obtain maximal computation sharing the problem is formulated using a graph in which vertices and edges represent coefficients and computational cost number of resources the multiplierless solution is obtained by solving a set cover problem on the vertices in the graph a simple polynomial run time algorithm based on a greedy approach is presented the proposed approach is compared with common subexpression elimination to show slightly better results and is combined with it for further reduction of complexity simulation results show that 50 60 complexity reduction is achieved by only applying the mrp algorithm and 70 complexity reduction is obtainable by combining it with common subexpression elimination under a delay constraint of two or three

a new approach to the design of discrete coefficient fir digital filters in this correspondence the iterative lagrange multiplier approach is proposed for designing discrete coefficient fir digital filters the method associates the conventional lagrange multiplier approach and a tree search algorithm for each branch of the tree the lagrange multiplier approach is used to optimize the remaining unquantized coefficients of the designed fir filter in the least squares sense when one or more of the coefficients takes on discrete values design examples including general low pass filters and nyquist filters are presented to demonstrate the effectiveness of the method also the method can be extended to design discrete coefficient 2 d fir filters

scattering of regularized long wave solitary waves abstract the lagrangian density for the regularized long wave equation also known as the bbm equation is presented using the trial function technique ordinary differential equations that describe the time dependence of the position of the peaks amplitudes and widths for the collision of two solitary waves are obtained these equations are analyzed in the born and equal width approximations and compared with numerical results obtained by direct integration utilizing the split step fast fourier transform method the computations show that collisions are inelastic and that production of solitary waves may occur

high order shape design sensitivity a unified approach abstract three basic analytical approaches have been proposed for the calculation of sensitivity derivatives in shape optimization problems the first approach is based on differentiation of the discretised equations the second approach is based on variation of the continuum equations and on the concept of material derivative the third approach is based upon the existence of a transformation that links the material coordinate system with a fixed reference coordinate system this is not restrictive since such a transformation is inherent to fem and bem implementations in this paper we present a generalization of the latter approach on the basis of a generic unified procedure for integration in manifolds our aim is to obtain a single unified compact expression to compute arbitrarily high order directional derivatives independent of the dimension of the material coordinates system and of the dimension of the elements special care has been taken on giving the final results in terms of easy to compute expressions and special emphasis has been made in holding recurrence and simplicity of intermediate operations the proposed scheme does not depend on any particular form of the state equations and can be applied to both direct and adjoint state formulations thus its numerical implementation in standard engineering codes should be considered as a straightforward process as an example a second order sensitivity analysis is applied to the solution of a 3d shape design optimization problem

a posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem the reciprocal theorem of betti and rayleigh or in other notions duality arguments are used to derive error estimators for the finite element approximation of various quantities including local variables like single displacements and stresses the proposed error estimator is evaluated solving the set of equations for an additional right hand side simply applying the energy norm error estimators two times furthermore a general h adaptive algorithm is introduced which allows us to optimize meshes with respect to different user specified variables the efficiency of the current approach is demonstrated for plate and shell examples

enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions patch recovery based on superconvergent derivatives and equilibrium spre an enhancement of the superconvergent patch recovery spr is studied for linear elasticity problems the paper also presents a further improvement for recovery of derivatives near boundaries spreb where either tractions or displacements are prescribed this is made by inclusion of weighted residual errors at boundary points in the patch recovery a pronounced improvement in the post processed gradients of the finite element solution is observed by this method

finite word length fir filter design using integer programming over a discrete coefficient space it is demonstrated that the improvement achieved by using integer programming over simple coefficient rounding in the design of finite impulse response fir filters with discrete coefficients is most significant when the discrete coefficient space is the powers of two space or when a specification is to be met with a given coefficient word length by increasing the filter length both minimax and least square error criteria are considered

a triangular finite element with local remeshing for the large strain analysis of axisymmetric solids in this work a three node triangular finite element with two degrees of freedom per node for the large strain elasto plastic analysis of axisymmetric solids is presented the formulation resorts to the adjacent elements to obtain a quadratic interpolation of the geometry over a patch of four elements from which an average deformation gradient is defined thus the element formulation falls within the framework of assumed strain elements or more precisely of f bar type formulations the in plane behavior of the element is similar to the linear strain triangle but without the drawbacks of the quadratic triangle e g contact or distortion sensitivity the element does not suffer of volumetric locking in problems with isochoric plastic flow and the implementation is simple it has been implemented in a finite element code with explicit time integration of the momentum equations and tools that allow the simulation of industrial processes the widely accepted multiplicative decomposition of the deformation gradient in elastic and plastic components is adopted here an isotropic material with non linear isotropic hardening has been considered two versions of the element have been implemented based on a total and an updated lagrangian formulation respectively some approximations have been considered in the latter formulation aimed to reduce the number of operations in order to increase numerical efficiency to consider bulk forming with large geometric changes an automatic local remeshing strategy has been developed several examples are considered to assess the element performance with and without remeshing

performance limit of finite wordlength fir digital filters in many practical situations it is necessary to represent the coefficients of a finite impulse response fir digital filter by a finite number of bits this not only degrades the filter frequency response but also introduces a theoretical limit on the performance of the filter derivation of a lower bound on filter degradation is the purpose of this paper we consider a general case of a length n filter with a discrete set of allowable coefficients a theorem that gives the lower bound on the increase in minimax approximation error that is caused by the finite wordlength restriction is presented its extension and application to filter design cases is demonstrated the importance of this bound is not only theoretical its practical effectiveness is shown in the algorithm for optimal finite wordlength fir filter design where it significantly reduces the amount of computation

an interpolation technique for computing the dft of a sparse sequence an interpolation technique for the approximate computation of the dft of a sparse sequence is presented this new method is more efficient than fft pruning particularly for long sequences where the effectiveness of fft pruning diminishes this interpolation method for computing the dft of a sparse sequence is very useful in filter design and spectrum analysis

special symmetries to standard riccati equations and applications by using symmetries associated to riccati equation in standard form sre we obtain a family which can be integrated by quadratures as a consequence we get a new integrability condition for the generalized riccati equation gre we illustrate the result with some examples and we give some applications in the solitons theory

exact and approximate algorithms for the filter design optimization problem the filter design optimization fdo problem is defined as finding a set of filter coefficients that yields a filter design with minimum complexity satisfying the filter constraints it has received a tremendous interest due to the widespread application of filters assuming that the coefficient multiplications in the filter design are realized under a shift adds architecture the complexity is generally defined in terms of the total number of adders and subtractors in this paper we present an exact fdo algorithm that can guarantee the minimum design complexity under the minimum quantization value but can only be applied to filters with a small number of coefficients we also introduce an approximate algorithm that can handle filters with a large number of coefficients using less computational resources than the exact fdo algorithm and find better solutions than existing fdo heuristics we describe how these algorithms can be modified to handle a delay constraint in the shift adds designs of the multiplier blocks and to target different filter constraints and filter forms experimental results show the effectiveness of the proposed algorithms with respect to prominent fdo algorithms and explore the impact of design parameters such as the filter length quantization value and filter form on the complexity and performance of filter designs

new periodic and soliton solutions for the generalized bbm and burgers bbm equations abstract in this paper we consider the benjamin bona mahony equation bbm and we obtain new exact solutions for it by using a generalization of the well known tanh coth method new periodic and soliton solutions for the generalized bbm and burgers bbm equations are formally derived

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

design of nonuniformly spaced linear phase fir filters using mixed integer linear programming an optimization problem for designing a nonuniformly spaced linear phase fir filter with minimal complexity is formulated and solved by mixed integer linear programming milp examples illustrate that the proposed method is useful for designing a wide range of filter types and can outperform subset selection based design methods

a polynomial time algorithm for designing fir filters with power of two coefficients this paper presents a polynomial time algorithm for designing digital filters with coefficients expressible as sums of signed power of two spt terms our proposal is based on an observation that under certain circumstances the realization cost of a filter with spt coefficients depends only on the total number of spt terms regardless of how the terms distribute among the coefficients therefore the number of spt terms for each coefficient is not necessarily limited to a fixed number instead they should be allowed to vary subject to a given number of total spt terms for the filter this provides the possibility of finding a better set of coefficients our algorithm starts with initializing all the quantized coefficient values to zero it chooses one spt term at a time and allocates it to the currently most deserving coefficient to minimize the l sup spl infin distance between the spt coefficients and their corresponding infinite wordlength values this process of allocating the spt terms is repeated until the total number of spt terms for the filter is equal to a prescribed number for each filter gain the time complexity is a second order polynomial in the number of coefficients to be optimized and is a first order polynomial in the filter wordlength

pollution error in the h version of the finite element method and the local quality of the recovered derivatives abstract in this paper we address the quality of the solution derivatives which are recovered from finite element solutions by local averaging schemes as an example we consider the zienkiewicz zhu superconvergent patch recovery scheme the zz spr scheme and we study its accuracy in the interior of the mesh for finite element approximations of solutions of laplace s equation in polygonal domains we will demonstrate the following 1 in general the accuracy of the derivatives recovered by the zz spr or any other local averaging scheme may not be higher than the accuracy of the derivatives computed directly from the finite element solution 2 if the mesh is globally adaptive i e it is nearly equilibrated in the energy norm then we can practically always gain in accuracy by employing the recovered derivatives instead of the derivatives computed directly from the finite element solution 3 it is possible to guarantee that the recovered solution derivatives have higher accuracy than the derivatives computed directly from the finite element solution in any patch of elements of interest by employing a mesh which is adaptive only with respect to the patch of interest i e it is nearly equilibrated in a weighted energy norm 4 in practice we are often interested in obtaining highly accurate derivatives or heat fluxes stresses etc only in a few critical regions which are identified by a preliminary analysis a grid which is adaptive only with respect to the critical regions of interest may be much more economical for this purpose because it may achieve the desired accuracy by employing substantially fewer degrees of freedom than a globally adaptive grid which achieves comparable accuracy in the critical regions

fir filter design over a discrete powers of two coefficient space fir digital filters with discrete coefficient values selected from the powers of two coefficient space are designed using the methods of integer programming the frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients both the weighted minimax and the weighted least square error criteria are considered using a weighted least square error criterion it is shown that it is possible to predict the improvement that can be expected when integer quadratic programming is used instead of simple coefficient rounding

stress constraints sensitivity analysis in structural topology optimization abstract sensitivity analysis is an essential issue in the structural optimization field the calculation of the derivatives of the most relevant quantities displacements stresses strains in optimum design of structures allows to estimate the structural response when changes in the design variables are introduced this essential information is used by the most frequent conventional optimization algorithms slp mma feasible directions in order to reach the optimal solution according to this idea the sensitivity analysis of the stress constraints in topology optimization problems is a crucial aspect to obtain the optimal solution when stress constraints are considered maximum stiffness approaches usually involve one linear constraint and one non linear objective function thus the computation of the required sensitivity analysis does not mean a crucial limitation however in the topology optimization problem with stress constraints efficient and accurate computation of the derivatives is needed in order to reach appropriate optimal solutions in this paper a complete analytic and efficient procedure to obtain the sensitivity analysis of the stress constraints in topology optimization of continuum structures is analyzed first order derivatives and second order directional derivatives of the stress constraints are analyzed and included in the optimization procedure in addition topology optimization problems usually involve thousands of design variables and constraints thus an efficient implementation of the algorithms used in the computation of the sensitivity analysis is developed in order to reduce the computational cost required finally the sensitivity analysis techniques presented in this paper are tested by solving some application examples

approximate wave solutions for generalized benjamin bona mahony burgers equations we consider solitary wave solutions of generalized benjamin bona mahony burgers equations shortly bbmb the decomposition method is proposed for the numerical solution subject to appropriate initial condition soliton solutions are constructed to show the nature of the solution the numerical solutions of our model equation are calculated in the form of convergence power series with easily computable components the decomposition method performs extremely well in terms of accuracy efficiently simplicity stability and reliability

high order sensitivity analysis in shape optimization problems abstract a formulation for high order directional differentiation of functions defined through integration is presented the formulation has been developed initially for sensitivity analysis in optimal shape design problems by the finite elements method however its application range is much wider explicit analytical expressions are given for sequential directional derivatives special emphasis has been made in holding recurrence and simplicity of intermediate operations the proposed scheme does not depend strongly on any particular form of the state equations and its numerical implementation in finite elements method programs can be considered easy and efficient as an example up to second order sensitivity techniques are applied to the optimization of a concrete roof structural analysis has been performed in linear elastic conditions with quadratic three dimensional elements for the discretization of the roof

a new adaptive remeshing scheme based on the sensitivity analysis of the spr point wise error estimation abstract this paper presents a formulation for the obtainment of the sensitivity analysis of a point wise error estimator with respect to the nodal coordinates using the adjoint state method the proposed point wise error estimator is based on the spr method the numerical accuracy of the presented sensitivity analysis has been tested by perturbing a mesh the capability of the presented sensitivity analysis for the detection of pollution error has also been tested a new adaptive remeshing strategy based on the sensitivity analysis of the point wise error estimation has been developed and tested this strategy produces very cheap meshes for the accurate evaluation of stresses at specific points

on the design of fir filters with powers of two coefficients fir filters with powers of two coefficients are attractive for cost effective implementations the performance of one such structure the difference routing digital filter 8 is discussed using an snr criterion an optimal algorithm to select the value of the filter coefficients is presented results indicate that a 2 3 db improvement in the snr can be obtained with this new approach in addition the study gives some insight into the relationship between the filter sampling rate the number of coefficients and the size of the coefficient alphabet in particular it is seen that a tradeoff between the filter sampling rate and the size of the coefficient alphabet exists