constrained least square design of fir filters without specified transition bands this paper puts forth the notion that explicitly specified transition bands have been introduced in the filter design literature in part as an indirect approach for dealing with discontinuities in the desired frequency response we suggest that the use of explicitly specified transition bands is sometimes inappropriate because to satisfy a meaningful optimality criterion their use implicitly assumes a possibly unrealistic assumption on the class of input signals this paper also presents an algorithm for the design of peak constrained lowpass fir filters according to an integral square error criterion that does not require the use of specified transition bands this rapidly converging robust simple multiple exchange algorithm uses lagrange multipliers and the kuhn tucker conditions on each iteration the algorithm will design linear and minimum phase fir filters and gives the best l sub 2 filter and a continuum of chebyshev filters as special cases it is distinct from many other filter design methods because it does not exclude from the integral square error a region around the cut off frequency and yet it overcomes the gibbs phenomenon without resorting to windowing or smoothing out the discontinuity of the ideal lowpass filter

boundary feedback stabilization for an unstable time fractional reaction diffusion equation in this paper we consider boundary feedback stabilization for unstable time fractional reaction diffusion equations new state feedback controls with actuation on one end are designed by the backstepping method for both dirichlet and neumann boundary controls by the riesz basis approach and the fractional lyapunov method we prove the existence and uniqueness and the mittag leffler stability for the closed loop systems for both cases the observers and the observer based output feedback are designed to stabilize the systems

further results on the boundedness of multidimensional systems a sufficient condition is derived in this paper for the boundedness of a linear time invariant lti multidimensional md dynamic system over a special class of frequency domains these frequency domains are able to include many practically adopted frequency domains such as fans rectangles etc as a special situation as well as to give an approximation with a tolerable accuracy to many other physically significant frequency domains like ellipsoids and diamonds this condition becomes also necessary when the prescribed frequency domain is path connected moreover it is expressed in a linear matrix inequality lmi form and can be directly applied to the optimization of system output matrix and direct transmission matrix as well as the minimization of the frequency response bound in addition the dimension of the lmi is in the same order as that of the system matrices

state and output feedback boundary control for a coupled pde ode system abstract this note is devoted to stabilizing a coupled pde ode system with interaction at the interface first a state feedback boundary controller is designed and the system is transformed into an exponentially stable pde ode cascade with an invertible integral transformation where pde backstepping is employed moreover the solution to the resulting closed loop system is derived explicitly second an observer is proposed which is proved to exhibit good performance in estimating the original coupled system and then an output feedback boundary controller is obtained for both the state and output feedback boundary controllers exponential stability analyses in the sense of the corresponding norms for the resulting closed loop systems are provided the boundary controller and observer for a scalar coupled pde ode system as well as the solutions to the closed loop systems are given explicitly

sequential decoding of trellis codes at high spectral efficiencies a probabilistic algorithm is used to construct large constraint length trellis codes at high spectral efficiencies for use with sequential decoding linear trellis codes for two and four dimensional constellations with constraint lengths up to 19 are obtained these codes can achieve 180 spl deg rotational invariance to achieve full 90 spl deg rotational invariance nonlinear trellis codes for four dimensional constellations with constraint lengths up to 19 are obtained in both cases it is shown that the channel cutoff rate bound can be achieved using constraint lengths between 16 and 19 with sequential decoding at a bit error rate of 10 sup 5 10 sup 6 and that 4 9 5 8 db real coding gains can be achieved over uncoded systems with the same spectral efficiency

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

the role of linear semi infinite programming in signal adapted qmf bank design we consider the problem of designing a perfect reconstruction fir quadrature mirror filter qmf bank h g adapted to input signal statistics with the coding gain as the adaptation criterion maximization of the coding gain has so far been viewed as a difficult nonlinear constrained optimization problem it is shown that the coding gain depends only on the product filter p z h z h z sup 1 and this transformation leads to a stable class of linear optimization problems having finitely many variables and infinitely many constraints termed linear semi infinite programming sip problems the sought for original filter h z is obtained by deflation and spectral factorization of p z with the sip formulation every locally optimal solution is also globally optimal and can be computed using reliable numerical algorithms the natural regularity properties inherent in the sip formulation enhance the performance of these algorithms we present a comprehensive theoretical analysis of the sip problem and its dual characterize the optimal filters and analyze uniqueness and sensitivity issues all these properties are intimately related to those of the input signal and bring considerable insight into the nature of the adaptation process we present discretization and cutting plane algorithms and apply both methods to several examples

the dual parameterization approach to optimal least square fir filter design subject to maximum error constraints this paper is concerned with the design of linear phase finite impulse response fir digital filters for which the weighted least square error is minimized subject to maximum error constraints the design problem is formulated as a semi infinite quadratic optimization problem using a newly developed dual parameterization method in conjunction with the caratheodory s dimensional theorem an equivalent dual finite dimensional optimization problem is obtained the connection between the primal and the dual problems is established a computational procedure is devised for solving the dual finite dimensional optimization problem the optimal solution to the primal problem can then be readily obtained from the dual optimal solution for illustration examples are solved using the proposed computational procedure

probabilistic construction of large constraint length trellis codes for sequential decoding probabilistic algorithms are given for constructing good large constraint length trellis codes for use with sequential decoding that can achieve the channel cutoff rate bound at a bit error rate ber of 10 sup 5 10 sup 6 the algorithms are motivated by the random coding principle that an arbitrary selection of code symbols will produce a good code with high probability one algorithm begins by choosing a relatively small set of codes randomly the error performance of each of these codes is evaluated using sequential decoding and the code with the best performance among the chosen set is retained another algorithm treats the code construction as a combinatorial optimization problem and uses simulated annealing to direct the code search trellis codes for 8 psk and 16 qam constellations with constraint lengths v up to 20 are obtained simulation results with sequential decoding show that these codes reach the channel cutoff rate bound at a ber of 10 sup 5 10 sup 6 and achieve 5 0 6 35 db real coding gains over uncoded systems with the same spectral efficiency and up to 2 0 db real coding gains over 64 state trellis codes using viterbi decoding

shaping multidimensional signal spaces i optimum shaping shell mapping the structure of the regions which provide the optimum tradeoff between gamma sub s shaping gain and cer constellation expansion ratio and between gamma sub s and par peak to average power ratio in a finite dimensional space is introduced analytical expressions are derived for the corresponding tradeoff curves in general the initial parts of the curves have a steep slope this means that an appreciable portion of the maximum shaping gain corresponding to a spherical region can be achieved with a small value of cer sub s par the technique of shell mapping is introduced this is a change of variable which maps the optimum shaping region to a hypercube truncated within a simplex this mapping is a useful tool in computing the performance and also in facilitating the addressing of the optimum shaping region using the shell mapping a practical addressing scheme is presented that achieves a point on the optimum tradeoff curves for dimensionalities around 12 the point achieved is located near the knee of the corresponding tradeoff curve for larger dimensionalities a general shaping region with two degrees of freedom is used this region provides more flexibility in selecting the tradeoff point

generalized positiveness of spatially interconnected systems over quadratically constrained frequency domains abstract generalized positiveness is investigated in this paper for a spatially interconnected system sis results of 7 are corrected and extended to a more general frequency domain and to more complicated requirements on the frequency response of a sis based on an equivalent characterization of the interested frequency domain a linear matrix inequality lmi based sufficient condition is derived for the generalized positiveness of a sis over a frequency domain described by several matrix valued quadratic functions moreover using the separability property of convex sets situations have also been clarified under which this sufficient condition becomes also necessary

symmetric orthogonal complex valued filter bank design by semidefinite programming a new design method for complex valued two channel finite impulse response fir filter banks with both orthogonality and symmetry properties is developed based on a novel linear matrix inequality lmi characterization of trigonometric curves the optimal design of perfect reconstruction filter banks is cast into a semidefinite programming sdp problem the dimension of the resulting sdp problem is further reduced by exploiting convex duality consequently the globally optimal solution can be found for any practical filter length and desired regularity order

derivative controlled design of linear phase fir filters via waveform moments a new method for designing linear phase finite impulse response fir filters is proposed by using the blockwise waveform moments the proposed method yields linear phase fir filters whose magnitude response and its derivatives to a certain order take the prescribed values at equally spaced frequency points the design procedure only needs to solve a system of linear equations whose size is slightly smaller than the degree of the resulting filter in addition the inversion of the linear equations can be essentially precomputed therefore the proposed design method is computationally efficient in particular for some important cases i e the maximally flat r regular l sup th band fir filters a closed form formula can be obtained it is also shown that the resulting r regular l sup th band fir filters have the zero intersymbol interference property

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

linear matrix inequality formulation of spectral mask constraints with applications to fir filter design the design of a finite impulse response fir filter often involves a spectral mask that the magnitude spectrum must satisfy the mask specifies upper and lower bounds at each frequency and hence yields an infinite number of constraints in current practice spectral masks are often approximated by discretization but in this paper we derive a result that allows us to precisely enforce piecewise constant and piecewise trigonometric polynomial masks in a finite and convex manner via linear matrix inequalities while this result is theoretically satisfying in that it allows us to avoid the heuristic approximations involved in discretization techniques it is also of practical interest because it generates competitive design algorithms based on interior point methods for a diverse class of fir filtering and narrowband beamforming problems the examples we provide include the design of standard linear and nonlinear phase fir filters robust chip waveforms for wireless communications and narrowband beamformers for linear antenna arrays our main result also provides a contribution to system theory as it is an extension of the well known positive real and bounded real lemmas

backstepping control of coupled linear parabolic pides with spatially varying coefficients this paper considers the backstepping design of state feedback controllers for coupled linear parabolic partial integro differential equations pides of volterra type with distinct diffusion coefficients spatially varying parameters and mixed boundary conditions the corresponding target system is a cascade of parabolic pdes with local couplings allowing a direct specification of the closed loop stability margin the determination of the state feedback controller leads to kernel equations which are a system of coupled linear second order hyperbolic pides with spatially varying coefficients and rather unusual boundary conditions by extending the method of successive approximations for the scalar case to the considered system class the well posedness of these kernel equations is verified by providing a constructive solution procedure this results in a systematic method for the backstepping control of coupled parabolic pides as well as pdes the applicability of the new backstepping design method is confirmed by the stabilization of two coupled parabolic pides with dirichlet robin unactuated boundaries and a coupled neumann actuation

boundary control of coupled reaction advection diffusion systems with spatially varying coefficients recently the problem of boundary stabilization for unstable linear constant coefficient coupled reaction diffusion systems was solved by means of the backstepping method the extension of this result to systems with advection terms and spatially varying coefficients is challenging due to complex boundary conditions that appear in the equations verified by the control kernels in this technical note we address this issue by showing that these equations are essentially equivalent to those verified by the control kernels for first order hyperbolic coupled systems which were recently found to be well posed the result therefore applies in this case allowing us to prove h 1 stability for the closed loop system it also unveils a previously unknown connection between backstepping kernels for coupled parabolic and hyperbolic problems

efficient large scale filter filterbank design via lmi characterization of trigonometric curves many filter and filterbank design problems can be posed as the optimization of linear or convex quadratic objectives over trigonometric semi infinite constraints recent advances in design methodology are based on various linear matrix inequality lmi characterizations of the semi infinite constraints and semidefinite programming sdp solutions despite these advances the design of filters of several hundredth order which typically arise in multicarrier communication and signal compression cannot be accommodated this hurdle is due mainly to the large number of additional variables incurred in the lmi characterizations this paper proposes a novel lmi characterization of the semi infinite constraints that involves additional variables of miminal dimensions consequently the design of high order filters required in practical applications can be achieved examples of designs of up to 1200 tap filters are presented to verify the viability of the proposed approach

tracking control for boundary controlled parabolic pdes with varying parameters combining backstepping and differential flatness the combination of backstepping based state feedback control and flatness based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion convection reaction system with spatially and temporally varying parameters and nonlinear boundary input for this in a first step the backstepping transformation is utilized to determine a state feedback controller which transforms the original distributed parameter system into an appropriately chosen exponentially stable distributed parameter target system of a significantly simpler structure in a second step the flatness property of the target system is exploited in order to determine the feedforward controller which allows us to realize the tracking of suitably prescribed trajectories for the system output this results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion convection reaction system with varying parameters whose applicability and tracking performance is evaluated in simulation studies

algorithmic construction of trellis codes an algorithmic approach is proposed whereby long convolutional codes of rate r sub c k n can easily be constructed for any chosen signal constellation in signal space these algorithms are iterative and in each step a number of candidate codes are found which locally maximize the distance hamming or euclidean between the codewords the result is not necessarily a free distance optimizing code however since the construction complexity can be chosen optimal codes are quite frequently found the codes ae constructed such that a rapid growth of the column distance is achieved a method of combining two codes into a single code of twice the constraint length is also presented

new rotationally invariant four dimensional trellis codes two new classes of rotationally invariant trellis codes are constructed a simple method is used to check the rotational invariance of a given code in the process of searching for optimum trellis codes a class of linear trellis codes with constraint lengths 2 9 using four dimensional constellations is presented simulation results show that a 180 spl deg rotationally invariant constraint length 8 linear trellis code achieves about 0 4 db real coding gain compared to the best constraint length 6 code while the trellis complexity is only four times that of the constraint length 6 code on the other hand the constraint length 6 code that has been adopted for use in the v 34 28 8 kbit s modem standard has the same 0 4 db real coding gain compared to a constraint length 4 code which has also been adopted for the standard but it requires sixteen times the trellis complexity a class of fully rotationally invariant nonlinear trellis codes with constraint lengths 6 11 is also presented simulation results show that a 90 spl deg rotationally invariant constraint length 8 nonlinear trellis code performs almost as well as the best linear code

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

sphere bound achieving coset codes and multilevel coset codes a simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array l and its error probability on an additive white gaussian noise awgn channel it is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding including certain binary lattices these codes have structure of the kind that has been found to be useful in practice capacity curves and design guidance for practical codes are given exponential error bounds for coset codes are developed generalizing poltyrev s 1994 bounds for lattices these results are based on the channel coding theorems of information theory rather than the minkowski hlawka theorem of lattice theory

fir filter design by convex optimization using directed iterative rank refinement algorithm the advances in convex optimization techniques have offered new formulations of design with improved control over the performance of fir filters by using lifting techniques the design of a length l fir filter can be formulated as a convex semidefinite program sdp in terms of an l times l matrix that must be rank 1 although this formulation provides means for introducing highly flexible design constraints on the magnitude and phase responses of the filter convex solvers implementing interior point methods almost never provide a rank 1 solution matrix to obtain a rank 1 solution we propose a novel directed iterative rank refinement dirr algorithm where at each iteration a matrix is obtained by solving a convex optimization problem the semidefinite cost function of that convex optimization problem favors a solution matrix whose dominant singular vector is on a direction determined in the previous iterations analytically it is shown that the dirr iterations provide monotonic improvement and the global optimum is a fixed point of the iterations over a set of design examples it is illustrated that the dirr requires only a few iterations to converge to an approximately rank 1 solution matrix the effectiveness of the proposed method and its flexibility are also demonstrated for the cases where in addition to the magnitude constraints the constraints on the phase and group delay of filter are placed on the designed filter

mittag leffler convergent backstepping observers for coupled semilinear subdiffusion systems with spatially varying parameters abstract the purpose of this paper is to investigate the observer based boundary output feedback control for subdiffusion processes governed by coupled semilinear time fractional diffusion systems tfdss with spatially varying parameters for this backstepping technique is used to mittag leffler stabilize the coupled semilinear observer error dynamic systems we then design an observer based output feedback controller at the right boundary to realize the mittag leffler stability of the closed loop systems at hand a numerical example is finally included to test our methods

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

boundary control of coupled reaction diffusion processes with constant parameters the problem of boundary stabilization is considered for some classes of coupled parabolic linear pdes of the reaction diffusion type with reference to n coupled equations each one equipped with a scalar boundary control input a state feedback law is designed with actuation at only one end of the domain and exponential stability of the closed loop system is proven the treatment is addressed separately for the case in which all processes have the same diffusivity and for the more challenging scenario where each process has its own diffusivity and a different solution approach has to be taken the backstepping method is used for controller design and particularly the kernel matrix of the transformation is derived in explicit form of series of bessel like matrix functions by using the method of successive approximations to solve the corresponding pde thus the proposed control laws become available in explicit form additionally the stabilization of an underactuated system of two coupled reaction diffusion processes is tackled under the restriction that only a scalar boundary input is available capabilities of the proposed synthesis and its effectiveness are supported by numerical studies made for three coupled systems with distinct diffusivity parameters and for underactuated linearized dimensionless temperature concentration dynamics of a tubular chemical reactor controlled through a boundary at low fluid superficial velocities when convection terms become negligible

a novel adaptive beamformer based on semidefinite programming sdp with magnitude response constraints a novel robust adaptive beamformer formulated as a semidefinite programming sdp problem is proposed in this paper with new constraints on the magnitude response the beamwidth and response ripple of the robust response region can be well controlled moreover only a small part of these inequality constraints on the magnitude response are active during optimization so that few degrees of freedom dofs of the adaptive beamformer are consumed consequently the resultant beamformer has significant improvement on signal to interference plus noise ratio sinr an important problem in the proposed beamformer is how to generate the array weight vector from the optimal semidefinite matrix in this paper a method utilizing the extended spectral factorization method is proposed to solve this problem simple implementation flexible performance control as well as significant sinr enhancement support the practicability of the proposed method

on the extended luenberger type observer for semilinear distributed parameter systems the design of an extended luenberger observer is considered to solve the state observation problem for semilinear distributed parameter systems for this a backstepping based technique is proposed for the design of the output injection weights by making use of the extended linearization of the semilinear observer error system with respect to the observer state stability of both the linearized and the semilinear observer error dynamics is analyzed theoretically moreover an efficient sample and hold implementation is considered to improve the computational efficiency of the observer design simulation examples are provided for a bistable semilinear partial differential equation and the simplified model of a bioreactor with monod kinetics

lmi stability conditions for fractional order systems after an overview of the results dedicated to stability analysis of systems described by differential equations involving fractional derivatives also denoted fractional order systems this paper deals with linear matrix inequality lmi stability conditions for fractional order systems under commensurate order hypothesis it is shown that a direct extension of the second lyapunov s method is a tedious task if the fractional order n is such that 0 n 1 the stability domain is not a convex region of the complex plane however through a direct stability domain characterization three lmi stability analysis conditions are proposed the first one is based on the stability domain deformation and the second one on a characterization of the instability domain which is convex the third one is based on generalized lmi framework these conditions are applied to the gain margin computation of a crone suspension

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

trellis coding with multidimensional qam signal sets trellis coding using multidimensional quadrature amplitude modulation qam signal sets is investigated finite size 2d signal sets are presented that have minimum average energy are 90 degrees rotationally symmetric and have from 16 to 1024 points the best trellis codes using the finite 16 qam signal set with two four six and eight dimensions are found by computer search the multidimensional multi d signal set is constructed from the 2 d signal set the best moderate complexity trellis codes for infinite lattices with two four six and eight dimensions are also found the minimum free squared euclidean distance and number of nearest neighbors for these codes were used as the selection criteria many of the multi d codes are fully rotationally invariant and give asymptotic coding gains up to 6 0 db from the infinite lattice codes the best codes for transmitting j j 1 4 j 1 3 j 1 2 j 2 3 and j 3 4 b sym j an integer are presented

flatness based trajectory planning for diffusion reaction systems in a parallelepipedon a spectral approach spectral analysis is considered for the flatness based solution of the trajectory planning problem for a boundary controlled diffusion reaction system defined on a 1 r dimensional parallelepipedon by exploiting the riesz spectral properties of the system operator it is shown that a suitable reformulation of the resolvent operator allows a systematic introduction of a basic output which yields a parametrization of both the system state and the boundary input in terms of differential operators of infinite order their convergence is verified for both infinite dimensional and finite dimensional actuator configurations by restricting the basic output to certain gevrey classes involving non analytic functions with this a systematic approach is introduced for basic output trajectory assignment and feedforward tracking control towards the realization of finite time transitions between stationary profiles

efficient design of orthonormal wavelet bases for signal representation the efficient representation of a signal as a linear combination of elementary atoms or building blocks is central to much signal processing theory and many applications wavelets provide a powerful flexible and efficiently implementable class of such atoms in this paper we develop an efficient method for selecting an orthonormal wavelet that is matched to a given signal in the sense that the squared error between the signal and some finite resolution wavelet representation of it is minimized since the squared error is not an explicit function of the design parameters some form of approximation of this objective is required if conventional optimization techniques are to be used previous approximations have resulted in nonconvex optimization problems which require delicate management of local minima in this paper we employ an approximation that results in a design problem that can be transformed into a convex optimization problem and efficiently solved constraints on the smoothness of the wavelet can be efficiently incorporated into the design we show that the error incurred in our approximation is bounded by a function that decays to zero as the number of vanishing moments of the wavelet grows in our examples we demonstrate that our method provides wavelet bases that yield substantially better performance than members of standard wavelet families and are competitive with those designed by more intricate nonconvex optimization methods

robustly good trellis codes the relationship between the distance properties of trellis codes and the computational effort and error performance of sequential decoding is studied and optimum distance profile odp and optimum free distance ofd trellis codes are constructed for 8 psk and 16 qam modulation a comparison of the performance of both the odp and the ofd trellis codes reveals that neither class of codes results in the best trade off between error performance and computational effort when sequential decoding is used a new algorithm is then proposed to construct robustly good trellis codes for use with sequential decoding new trellis codes with asymptotic coding gains up to 6 66 db are obtained using this algorithm and the new codes achieve nearly the same free distances as the ofd codes and nearly the same distance profiles as the odp codes

optimized analog filter designs with flat responses by semidefinite programming analog filters constitute indispensable components of analog circuits inspired by recent advances in digital filter design this paper provides a flexible design for analog filters all pole filters have maximally flat passband so our design minimizes their passband distortion analogously maximally flat filters have maximally flat passband so our design maximizes their stopband attenuation its particular cases provide flexible alternatives to the classical counterparts semidefinite program sdp formulations for the posed filter design problems are presented which are efficiently solved by existing optimization software several examples and comparisons are provided to validate the viability of our design

meteor a constraint based fir filter design program it is proposed to specify a filter only in terms of upper and lower limits on the response find the shortest filter length which allows these constraints to be met and then find a filter of that order which is farthest from the upper and lower constraint boundaries in a minimax sense the simplex algorithm for linear programming is used to find a best linear phase fir filter of minimum length as well as to find the minimum feasible length itself the simplex algorithm while much slower than exchange algorithms also allows the incorporation of more general kinds of constraints such as concavity constraints which can be used to achieve very flat magnitude characteristics examples are given to illustrate how the proposed and common approaches differ and how the proposed approach can be used to design filters with flat passbands filters which meet point constraints minimum phase filters and bandpass filters with controlled transition band behavior

design of orthogonal pulse shapes for communications via semidefinite programming in digital communications orthogonal pulse shapes are often used to represent message symbols for transmission through a channel in this paper the design of such pulse shapes is formulated as a convex semidefinite programming problem from which a globally optimal pulse shape can be efficiently found the formulation is used to design filters that achieve a the minimal bandwidth for a given filter length b the minimal filter length for a given bandwidth c the maximal robustness to timing error for a given bandwidth and filter length bandwidth is measured either in spectral energy concentration terms or with respect to a spectral mask the effectiveness of the method is demonstrated by the design of waveforms with substantially improved performance over the chip waveforms specified in standards for digital mobile telecommunications

trellis shaping the author discusses trellis shaping a method of selecting a minimum weight sequence from an equivalence class of possible transmitted sequences by a search through the trellis diagram of a shaping convolutional code c sub s shaping gains on the order of 1 db may be obtained with simple four state shaping codes and with moderate constellation expansion the shaping gains obtained with more complicated codes approach the ultimate shaping gain of 1 53 db with a feedback free syndrome former for c sub s transmitted data can be recovered without catastrophic error propagation constellation expansion and peak to average energy ratio may be effectively limited by peak constraints with lattice theoretic constellations the shaping operation may be characterized as a decoding of an initial sequence in a channel trellis code by a minimum distance decoder for a shaping trellis code based on the shaping convolutional code and the set of possible transmitted sequences is then the set of code sequences in the channel trellis code that lie in the voronoi region of the trellis shaping code

fractional order systems and pi sup spl lambda d sup spl mu controllers dynamic systems of an arbitrary real order fractional order systems are considered the concept of a fractional order pi sup spl lambda d sup spl mu controller involving fractional order integrator and fractional order differentiator is proposed the laplace transform formula for a new function of the mittag leffler type made it possible to obtain explicit analytical expressions for the unit step and unit impulse response of a linear fractional order system with fractional order controller for both open and closed loops an example demonstrating the use of the obtained formulas and the advantages of the proposed pi sup spl lambda d sup spl mu controllers is given

efficient design of oversampled npr gdft filterbanks we propose a flexible efficient design technique for the prototype filter of an oversampled near perfect reconstruction npr generalized discrete fourier transform gdft filterbank such filterbanks have several desirable properties for subband processing systems that are sensitive to aliasing such as subband adaptive filters the design criteria for the prototype filter are explicit bounds derived herein on the aliased components in the subbands and the output the distortion induced by the filterbank and the imaged subband errors in the output it is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem which can be efficiently solved the proposed design technique provides an efficient and effective tool for exploring many of the inherent tradeoffs in the design of the prototype filter including the tradeoff between aliasing in the subbands and the distortion induced by the filterbank we calculate several examples of these tradeoffs and demonstrate that the proposed method can generate filters with significantly better performance than filters obtained using current design methods

backstepping observer based output feedback control for a class of coupled parabolic pdes with different diffusions abstract this paper aims to design a backstepping observer based output feedback controller for a class of coupled parabolic partial differential equations pdes with different diffusions the considered system is endowed with a sensor at the left boundary and an actuation at the right boundary firstly a backstepping observer is designed secondly compared to the existing literature a weaker condition is deduced to guarantee the stability of the plant system by means of a controller thirdly using the separation principle an observer based output feedback controller is set up based on the designed observer and controller finally the efficiency of the proposed method is shown by taking a simplified model of chemical tubular reactor

trajectory planning for boundary controlled parabolic pdes with varying parameters on higher dimensional spatial domains the flatness based design of a feedforward tracking control is considered for the solution of the trajectory planning problem for a boundary controlled diffusion convection reaction system with spatially and temporally varying parameters defined on a 1 les m dimensional parallelepipedon with the nonlinear input being restricted to a m 1 dimensional hyperplane for this an implicit state and input parametrization in terms of a basic output is determined via a volterra type integral equation with operator kernel by recursively computing successive series coefficients a series solution of the integral equation is obtained whose absolute and uniform convergence is verified by restricting the system parameters and the basic output to a certain but broad gevrey class hence prescribing an admissible desired trajectory for the basic output directly yields the feedforward control by evaluating the input parametrization this results in a systematic procedure for trajectory planning and feedforward control design for boundary controlled parabolic distributed parameter systems defined on higher dimensional domains

boundedness of multidimensional filters over a prescribed frequency domain signal processing often requires the magnitude of a filter simultaneously upper and lower bounded on some specified frequency domains in this paper on the basis of the structure of the span of a multivariate matrix polynomial a sufficient condition is derived for the boundedness of a multidimensional multiple input multiple output mimo infinite impulse response iir filter over a cuboid frequency domain this condition is expressed through a linear matrix inequality lmi and can be proved to be less conservative than a condition derived from an upper bound of matrix structured singular value moreover using parameter dependent lmis and the linear fractional transformation structure of the filter two necessary and sufficient conditions are also obtained for this boundedness verification problem which are again expressed by lmis furthermore lmi based conditions are derived for filter output matrix and direct transmission matrix which are applicable to filter design numerical examples are included to illustrate the efficiency and characteristics of the derived theoretical results

peak constrained least squares optimization we presented the basic concepts for peak constrained least squares pcls optimization in previous papers we present advanced pcls optimization concepts in this paper this paper discusses only a few of the many ways that pcls design problems can be formulated we believe that the pcls optimality criterion can be customized to fit virtually any practical application for example pcls optimization can readily be used to design equalizers in the prefilter equalizer or interpolated fir implementations of filters

construction of trellis codes with a good distance profile systematic feedforward trellis codes for 8 psk and 16 qam modulation are constructed using a nested step by step algorithm which guarantees a good distance profile this makes the codes suitable for use with sequential decoding where a rapidly growing distance profile is needed to reduce the average number of computations in addition to having a good distance profile the new codes achieve asymptotic coding gains of up to 6 53 db a procedure based upon the fano 1963 algorithm fa is used to calculate the free distance of the new codes this procedure is very effective for finding the free distances of long trellis codes because of the computational and storage efficiency of the fa from a comparison of the new systematic feedforward codes with ungerboeck s 1982 1987 systematic feedback codes the authors conjecture that a systematic feedforward code of constraint length 2 spl nu can achieve the same free distance as a systematic feedback code of constraint length spl nu