analytic torsion and holomorphic determinant bundles i bott chern forms and analytic torsion we attach secondary invariants to any acyclic complex of holomorphic hermitian vector bundles on a complex manifold these were first introduced by bott and chern bot c our new definition uses quillen s superconnections we also give an axiomatic characterization of these classes these results will be used in bgs2 and bgs3 to study the determinant of the cohomology of a holomorphic vector bundle

a causality in variance test and its application to financial market prices abstract this paper develops a test for causality in variance the test is based on the residual cross correlation function ccf and is robust to distributional assumptions asymptotic normal and asymptotic 2 statistics are derived under the null hypothesis of no causality in variance monte carlo results indicate that the proposed ccf test has good empirical size and power properties two empirical examples illustrate that the causality test yields useful information on the temporal dynamics and the interaction between two time series

reproducing kernel structure and sampling on time warped spaces with application to warped wavelets time warped signal spaces have received attention in the literature among the topics of particular interest are sampling of time warped signals and signal analysis using warped analysis functions including wavelets this correspondence introduces a reproducing kernel rk structure for time warped signal spaces that unifies multiple perspectives on sampling in such spaces

optimality conditions for truncated laguerre networks presents optimality conditions for truncated laguerre networks both for continuous time and for discrete time contrary to the current approach no assumption is made about the whiteness of the power spectrum of the input signal curiously the results obtained have the same form as those published for the more restrictive case where the input signal is an impulse at the time origin or white noise

calculating discriminants by higher direct images the author uses the homological algebra to construct for any line bundle y on a nonsingular projective variety x the complex if s whose determinant is equal to the equation of the dual variety xv this generalizes the cayley koszul complexes defined by gelfand kapranov and zelevinski the formulas for the codimension and degree of xv in terms of complexes f y are given in the second part of the article the general technique is applied to classical discriminants and hyperdeterminants this paper consists of two parts in the first part 1 and 2 we give the method for calculating generalized discriminants considered by gelfand kapranov and zelevinski cf g k z the generalized discriminant is defined for any nonsingular projective variety x as the defining equation of the dual variety xv the method for calculating these equations introduced here uses the conormal construction and the technique of higher direct images for each line bundle y on x we define the canonical complex if s obtained by pushing down the twisted koszul resolutions associated to the canonical desingularisation of the dual variety xv the complex if y allows to calculate explicitly the degree of the discriminant and give the expression for it in terms of buchsbaum eisenbud multipliers associated to if y the general technique is described in 1 where all general formulas are proved section 2 deals with the case of g discriminants they occur when the nonsingular variety x is the g orbit of the highest weight vector in the irreducible representation of the reductive group g in the second part 3 and 4 we investigate the determinantal expressions of the discriminants they arise naturally in the context of the complexes f y if the complex 1f 2 has only two terms it reduces to a matrix in such cases the discriminant becomes the determinant of this matrix section 3 deals with the case of the discriminant of a homogeneous polynomial of degree m classically such formulas were known for the case of two variables sylvester and bezout formulas and three variables which is treated in the book of salmon s in 3 we give a list of such formulas in the case of two variables this list includes the sylvester expression 3 2 m arbitrary a 1 and bezout expression 3 2 m arbitrary a m 2 moreover these formulas appear as the extreme cases of the whole series of determinantal expressions of similar type section 3 3 deals with the case of three variables received by the editors march 27 1992 and in revised form october 5 1992 1991 mathematics subject classification primary 13d25 14n05 secondary 13d02 14m15 15a72 1994 american mathematical society 0002 9947 94 1 00 25 per page

on approximation of stable linear dynamical systems using laguerre and kautz functions approximation of stable linear dynamical systems by means of so called laguerre and kautz functions which are the laplace transforms of a class of orthonormal exponentials is studied since the impulse response of a stable finite dimensional linear dynamical system can be represented by a sum of exponentials times polynomials it seems reasonable to use basis functions of the same type assuming that the transfer function of a system is bounded and analytic outside a given disc it is shown that laguerre basis functions are optimal in a mini max sense this result is extended to the two parameter kautz functions which can have complex poles while the poles of laguerre functions are restricted to the real axis by conformai mapping techniques the two parameter kautz approximation problem is recast as two laguerre approximation problems thus the well developed theory of laguerre functions can be applied to analyze kautz approximations unilateral shifts are used to further develop the connection between laguerre functions and kautz functions results on 2 and approximation using kautz models are given furthermore the weighted l2 kautz approximation problem is shown to be equivalent to solving a block toeplitz matrix equation

dual mode predictive control algorithm for constrained hammerstein systems in the process industry there exist many systems which can be approximated by a hammerstein model moreover these systems are usually subjected to input magnitude constraints in this paper a multi channel identification algorithm mcia is proposed in which the coefficient parameters are identified by least squares estimation lse together with a singular value decomposition svd technique compared with traditional single channel identification algorithms the present method can enhance the approximation accuracy remarkably and provide consistent estimates even in the presence of coloured output noises under relatively weak assumptions on the persistent excitation pe condition of the inputs then to facilitate the following controller design this mcia is converted into a two stage single channel identification algorithm ts scia which preserves most of the advantages of mcia with this ts scia as the inner model a dual mode non linear model predictive control nmpc algorithm is developed in detail over a finite horizon an optimal input profile found by solving a open loop optimal control problem drives the non linear system state into the terminal invariant set afterwards a linear output feedback controller steers the state to the origin asymptotically in contrast to the traditional algorithms the present method has a maximal stable region a better steady state performance and a lower computational complexity finally simulation results on a heat exchanger are presented to show the efficiency of both the identification and the control algorithms

frequency warped filter banks and wavelet transforms a discrete time approach via laguerre expansion we introduce a new generation of perfect reconstruction filter banks that can be obtained from classical critically sampled filter banks by means of frequency transformations the novel filters are laguerre type iir filters that can be directly derived and designed from ordinary orthogonal or biorthogonal filter banks generalized downsampling and upsampling operators based on dispersive delay lines are the building blocks of our structures by iterating the filter banks we construct new orthogonal and complete sets of wavelets whose passbands are not octave spaced and may be designed by selecting a single parameter

optimum laguerre networks for a class of discrete time systems an analytical approach is introduced that directly yields the optimum value of the laguerre parameter b this is achieved by minimizing the mean square error between the unit sample response of the given discrete system and that of its laguerre counterpart it is shown that laguerre networks are best suited to realized systems whose exponential unit sample responses die down rapidly

choice of free parameters in expansions of discrete time volterra models using kautz functions this work tackles the problem of modeling nonlinear systems using volterra models based on kautz functions the drawback of requiring a large number of parameters in the representation of these models can be circumvented by describing every kernel using an orthonormal basis of functions such as the kautz basis the resulting model so called wiener volterra model can be truncated into a few terms if the kautz functions are properly designed the underlying problem is how to select the free design complex poles that fully parameterize these functions a solution to this problem has been provided in the literature for linear systems which can be represented by first order volterra models a generalization of such strategy focusing on volterra models of any order is presented in this paper this problem is solved by minimizing an upper bound for the error resulting from the truncation of the kernel expansion into a finite number of functions the aim is to minimize the number of two parameter kautz functions associated with a given series truncation error thus reducing the complexity of the resulting finite dimensional representation the main result is the derivation of an analytical solution for a sub optimal expansion of the volterra kernels using a set of kautz functions

exact search directions for optimization of linear and nonlinear models based on generalized orthonormal functions a novel technique for selecting the poles of orthonormal basis functions obf in volterra models of any order is presented it is well known that the usual large number of parameters required to describe the volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions such a representation results in the so called obf volterra model which has a wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the volterra polynomial series aiming at optimizing the poles that fully parameterize the orthonormal bases the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back propagation through time technique the expressions relative to the kautz basis and to generalized orthonormal bases of functions gobf are addressed the ones related to the laguerre basis follow straightforwardly as a particular case the main innovation here is that the dynamic nature of the obf filters is fully considered in the gradient computations these gradients provide exact search directions for optimizing the poles of a given orthonormal basis such search directions can in turn be used as part of an optimization procedure to locate the minimum of a cost function that takes into account the error of estimation of the system output the levenberg marquardt algorithm is adopted here as the optimization procedure unlike previous related work the proposed approach relies solely on input output data measured from the system to be modeled i e no information about the volterra kernels is required examples are presented to illustrate the application of this approach to the modeling of dynamic systems including a real magnetic levitation system with nonlinear oscillatory behavior

blind input initial state and system identification of simo laguerre systems laguerre filters have infinite impulse responses iirs but with finite tapped delay line parameterizations this paper investigates subspace based blind identification of laguerre filter tap coefficients the internal filter state and the input given only noisy observations of the output this paper deals only with single input multiple output simo laguerre models a state space model for the simo laguerre system is derived from which blind estimation algorithms are developed as in the finite impulse response fir case the laguerre filter taps coefficients can be estimated from the column space of a certain hankel matrix constructed from noisy output observations whereas the internal state and input can be estimated from the row space by exploiting state space structure while not exactly uniquely identifiable conditions are given for which the tap coefficients the internal state and the input can be determined to within a multiplicative scalar factor

a comparison of performance of three orthogonal polynomials in extraction of wide band response using early time and low frequency data the objective of this paper is to generate a wideband and temporal response of three dimensional composite structures by using a hybrid method that involves generation of early time and low frequency information the data in these two separate time and frequency domains are mutually complementary and contain all the necessary information for a sufficient record length utilizing a set of orthogonal polynomials the time domain signal be it the electric or the magnetic currents or the near far scattered electromagnetic field could be expressed in an efficient way as well as the corresponding frequency domain responses the available data is simultaneously extrapolated in both domains computational load for electromagnetic analysis in either domain time or frequency can be thus significantly reduced three orthogonal polynomial representations including hermite polynomial laguerre function and bessel function are used in this approach however the performance of this new method is sensitive to two important parameters the scaling factor l sub 1 and the expansion order n it is therefore important to find the optimal parameters to achieve the best performance a comparison is presented to illustrate that for the classes of problems dealt with the choice of the laguerre polynomials has the best performance as illustrated by a typical scattering example from a dielectric hemisphere

adaptive laguerre lattice filters adaptive laguerre based filters provide an attractive alternative to adaptive fir filters in the sense that they require fewer parameters to model a linear time invariant system with a long impulse response we present an adaptive laguerre lattice structure that combines the desirable features of the laguerre structure i e guaranteed stability unique global minimum and small number of parameters m for a prescribed level of modeling error with the numerical robustness and low computational complexity of adaptive fir lattice structures the proposed configuration is based on an extension to the iir case of the fir lattice filter it is a cascade of identical sections but with a single pole all pass filter replacing the delay element used in the conventional fir lattice filter we utilize this structure to obtain computationally efficient adaptive algorithms o m computations per time instant our adaptive laguerre lattice filter is an extension of the gradient adaptive lattice gal technique and it demonstrates the same desirable properties namely 1 excellent steady state behavior 2 relatively fast initial convergence comparable with that of an rls algorithm for laguerre structure and good numerical stability simulation results indicate that for systems with poles close to the unit circle where an adaptive fir model of very high order would be required to meet a prescribed modeling error an adaptive laguerre lattice model of relatively low order achieves the prescribed bound after just a few updates of the recursions in the adaptive algorithm

system identification using kautz models in this paper the problem of approximating a linear time invariant stable system by a finite weighted sum of given exponentials is considered system identification schemes using laguerre models are extended and generalized to kautz models which correspond to representations using several different possible complex exponentials in particular linear regression methods to estimate this sort of model from measured data are analyzed the advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters the subsequent analysis is based on the result that the corresponding linear regression normal equations have a block toeplitz structure several results on transfer function estimation are extended to discrete kautz models for example asymptotic frequency domain variance expressions

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

sampling expansions for multiband signals the class b i of finite energy signals bandlimited to a set i is considered where i denotes a finite union of disjoint open intervals bands on the real frequency axis if such a signal is sampled uniformly constant intersample spacing t it is shown that the following five propositions are equivalent 1 any signal in b i is uniquely determined from its uniform samples taken at the rate 1 t samples s 2 the set of complex exponentials e in omegat min infin max infin is complete on the set i 3 the translated sets omega k sigma omega epsiloni with 2 t do not intersect i for any k neq 0 4 each signal in b i possesses a mean square convergent sampling expansion in terms of its samples at rate 1 t samples s 5 a generalized parseval relation holds for each pair of signals in b i

the gamma filter a new class of adaptive iir filters with restricted feedback generalized feedforward filters a class of adaptive filters that combines attractive properties of finite impulse response fir filters with some of the power of infinite impulse response iir filters are described a particular case the gamma filter generalizes widrow s adaptive transversal filter adaline to an infinite impulse response filter yet the stability condition for the gamma filter is trivial and lms adaptation is of the same computational complexity as the conventional transversal filter structure preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter the authors extend the wiener kopf equation to the gamma filter and develop some analysis tools

brief constrained robust predictive controller for uncertain processes modeled by orthonormal series functions the present work focuses on robust predictive control rpc of uncertain processes and proposes a new approach based on orthonormal series function modeling in such unstructured modeling the output signal is described as a weighted sum of orthonormal functions that uses approximative information about the time constant of the process due to an efficient uncertainty representation this kind of modeling is advantageous in the rpc context even for constrained systems and processes with integral action the stability of the closed loop system is guaranteed by the setting of sufficient conditions for the selection of the controller prediction horizon simulation results are presented to illustrate the performance of this new rpc algorithm

technical communique a note on the optimal expansion of volterra models using laguerre functions this work tackles the problem of expanding volterra models using laguerre functions a strict global optimal solution is derived when each multidimensional kernel of the model is decomposed into a set of independent orthonormal bases each of which parameterized by an individual laguerre pole intended for representing the dominant dynamic of the kernel along a particular dimension it is proved that the solution derived minimizes the upper bound of the squared norm of the error resulting from the practical truncation of the laguerre series expansion into a finite number of functions this is an extension of the results in campello favier and amaral 2004 optimal expansions of discrete time volterra models using laguerre functions automatica 40 815 822 where an optimal solution was obtained for the usual yet particular case in which a single laguerre pole is used for expanding a given kernel along all its dimensions it is also proved that the particular and extended solutions are equivalent to each other when the volterra kernels are symmetric

a generalized orthonormal basis for linear dynamical systems in many areas of signal system and control theory orthogonal functions play an important role in issues of analysis and design in this paper it is shown that there exist orthogonal functions that in a natural way are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l sub 2sup n to this end use is made of balanced realizations of inner transfer functions the orthogonal functions can be considered as generalizations of for example the pulse functions laguerre functions and kautz functions and give rise to an alternative series expansion of rational transfer functions it is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion i e to obtain a good approximation by retaining only a finite number of expansion coefficients consequences for identification of expansion coefficients are analyzed and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients

improved method for optimum choice of free parameter in orthogonal approximations we report on our investigations to choose a free parameter to minimize the error energy when approximating a given signal with orthogonal basis functions this method requires limited knowledge of the signal to be approximated and has a low computational cost

nonuniform fast fourier transforms using min max interpolation the fast fourier transform fft is used widely in signal processing for efficient computation of the ft of finite length signals over a set of uniformly spaced frequency locations however in many applications one requires nonuniform sampling in the frequency domain i e a nonuniform ft several papers have described fast approximations for the nonuniform ft based on interpolating an oversampled fft this paper presents an interpolation method for the nonuniform ft that is optimal in the min max sense of minimizing the worst case approximation error over all signals of unit norm the proposed method easily generalizes to multidimensional signals numerical results show that the min max approach provides substantially lower approximation errors than conventional interpolation methods the min max criterion is also useful for optimizing the parameters of interpolation kernels such as the kaiser bessel function

on the relationship between the enforced convergence criterion and the asymptotically optimal laguerre pole when approximating dynamic systems with laguerre basis functions lbfs it is important to tune the laguerre pole such that the expansion can be both parsimonious and accurate expressing the sum of squared errors sse as a function of the laguerre pole leads to an objective function that has many local minima and therefore cannot be optimized directly two alternative methods have been proposed in the literature an asymptotically optimal method and the enforced convergence criterion ecc in this paper a generalization of the ecc will be investigated such that in the limit minimizing this generalized ecc and computing the asymptotically optimal solution lead to the same laguerre pole moreover it will be proved that these generalized eccs are quasiconvex functions which means they can be efficiently minimized using numerical optimization techniques the concept of operator quasiconvexity is investigated and used to prove quasiconvexity of the ecc

on a result of gelfand kapranov and zelevinsky abstract in this paper we give new elementary proofs of basic results due to gelfand kapranov and zelevinsky which express discriminants and results in terms of determinants of direct images of stably twisted cayley koszul complexes of sheaves

tilings of the time frequency plane construction of arbitrary orthogonal bases and fast tiling algorithms the authors consider expansions which give arbitrary orthonormal tilings of the time frequency plane these differ from the short time fourier transform wavelet transform and wavelet packets tilings in that they change over time they show how this can be achieved using time varying orthogonal tree structures which preserve orthogonality even across transitions the method is based on the construction of boundary and transition filters these allow us to construct essentially arbitrary tilings time varying modulated lapped transforms are a special case where both boundary and overlapping solutions are possible with filters obtained by modulation they present a double tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency that is it is a joint optimization of time and frequency splitting the algorithm is optimal for additive cost functions e g rate distortion and results in time varying best bases the main application of which is for compression of nonstationary signals experiments on test signals are presented

dynamic siso and miso system approximations based on optimal laguerre models a general procedure based on the knowledge of the input and the output signals is proposed to approximate the prescribed linear time invariant lti systems by means of optimal laguerre models the main contribution of this paper is to apply the newton raphson s iterative technique to compute the so called optimal laguerre pole in a continuous time case or optimal time scale factor in a discrete time case and especially to show that the gradient and the hessian can be expressed analytically moreover the excitations used are not limited to the ones that ensure the orthogonality of the outputs of laguerre filters i e dirac delta or white noise as is usually done in existing methods however persistently exciting input signal s are used the proposed procedure will be directly formulated for siso systems siso systems being a special case with the number of inputs equal to one the proposed algorithm has direct applications in system identification model reduction and noisy modeling

online identification of the arx model expansion on laguerre orthonormal bases with filters on model input and output this article proposes a new representation of the arx models on independent and orthonormal laguerre bases by filtering the process input and output using laguerre orthonormal functions the resulting model entitled arx laguerre model ensures the parameter number reduction with a recursive and easy representation however this reduction is still subject to an optimal choice of the laguerre poles defining both laguerre bases therefore we propose an analytical solution to optimise the laguerre poles which depend on fourier coefficients defining the arx laguerre model and that are identified using the regularised square error the identification procedures of the laguerre poles and fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the arx laguerre model the proposed algorithm is tested on numerical simulation and validated on a benchmark system manufactured by feedback known as process trainer pt326

a hybrid genetic algorithm for estimating the optimal time scale of linear systems approximations using laguerre models we deal with the problem of finding the optimal time scale of the truncated laguerre series using numerical search techniques we develop a hybrid genetic algorithm ga to search the nonlinear multimodal squared error function that results from least squares approximations of the impulse response of causal linear time invariant stable systems the hybrid ga incorporates a newton raphson nr local optimizer for fast convergence to the global minimum point the proposed method competes favorably with the pure ga in solution accuracy the number of function evaluations being the same and with an established gradient directed optimization algorithm in number of function evaluations the solution accuracy being the same

wavelet based representations for a class of self similar signals with application to fractal modulation a potentially important family of self similar signals based upon a deterministic scale invariance characterization is introduced these signals which are referred to as dy homogeneous signals because they generalize the well known homogeneous functions have highly convenient representations in terms of orthonormal wavelet bases in particular wavelet representations can be exploited to construct orthonormal self similar bases for these signals the spectral and fractal characteristics of dy homogeneous signals make them appealing candidates for use in a number of applications as one potential example their use in a communications based context is considered specifically a strategy for embedding information into a dy homogeneous waveform on multiple time scales is developed this multirate modulation strategy called fractal modulation is potentially well suited for use with noisy channels of simultaneously unknown duration and bandwidth

the coding gain of multiplexed wavelet transforms evangelista 1994 1993 introduced the multiplexed wavelet transform mwt and pointed out its potential applications to the analysis synthesis processing and coding of pseudo periodic signals such as voiced speech and music coders based on the mwt have been shown to outperform the conventional subband coders when a reliable pitch parameter can be extracted from data in this paper we investigate the effects of uniform quantization of the mwt coefficients we compare the performance of the new coders with that of wt block dct and klt coders in terms of the coding gain achieved when optimal bit allocation schemes are adopted

discrete frequency warped wavelets theory and applications we extend the definition of dyadic wavelets to include frequency warped wavelets the new wavelets are generated and the transform computed in discrete time by alternating the laguerre transform with perfect reconstruction filterbanks this scheme provides the unique implementation of orthogonal or biorthogonal warped wavelets by means of rational transfer functions we show that the discrete time warped wavelets lead to well defined continuous time wavelet bases satisfying a warped form of the two scale equation the shape of the wavelets is not invariant by translation rather the wavelet translates are obtained from one another by allpass filtering we show that the phase of the delay element is asymptotically a fractal a feature of the warped wavelet transform is that the cut off frequencies of the wavelets may be arbitrarily assigned while preserving a dyadic structure the new transform provides an arbitrary tiling of the time frequency plane which can be designed by selecting as little as a single parameter this feature is particularly desirable in cochlear and perceptual models of speech and music where accurate bandwidth selection is an issue as our examples show by defining pitch synchronous wavelets based on warped wavelets the analysis of transients and denoising of inharmonic pseudo periodic signals is greatly enhanced

unitary equivalence a new twist on signal processing unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time frequency and scale implementation of these new tools involves simply preprocessing the signal by a unitary transformation performing standard processing on the transformed signal and then in some cases transforming the resulting output the resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and hence prove useful for representing and processing signals that are not well matched by current techniques as specific examples of this procedure we generalize linear time invariant systems orthonormal basis and frame decompositions and joint time frequency and time scale distributions these applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature

continuous time envelope constrained filter design via laguerre filters and spl hscr sub spl infin optimization methods the envelope constrained filtering problem is concerned with the design of a time invariant filter to process a given input signal such that the noiseless output of the filter is guaranteed to lie within a specified output mask while minimizing the noise gain of the filter an algorithm is developed to solve the continuous time envelope constrained filter design problem with the spl hscr sub spl infin norm of the filter as the cost and an orthonormal set of basis filters it is shown that the problem can be reformulated and solved as a constrained spl hscr sub spl infin model matching problem to illustrate the effectiveness of the design method two numerical examples are presented that deal with the design of equalization filters for digital transmission channels

an optimal expansion of volterra models using independent kautz bases for each kernel dimension a new solution for the problem of selecting poles of the two parameter kautz functions in volterra models is proposed in general a large number of parameters are required to represent the volterra kernels although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions such as the kautz basis this representation has a wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a non linear static mapping represented by the volterra series the resulting wiener volterra model can be truncated into fewer terms if the kautz functions are properly designed the underlying problem is how to select the arbitrary complex poles that fully parametrize these functions this problem has been approached in previous research by minimizing an upper bound for the error resulting from the truncation of the kernel expansion the present paper goes even further in that each multidimensional kernel is decomposed into a set of independent kautz bases each of which is parametrized by an individual pair of conjugate kautz poles intended to represent the dominant dynamic of the kernel along a particular dimension an analytical solution for one of the kautz parameters valid for volterra models of any order is derived a simulated example is presented to illustrate these theoretical results the same approach is then used to model a real non linear magnetic levitation system with oscillatory behaviour

brief paper choice of free parameters in expansions of discrete time volterra models using kautz functions this work tackles the problem of modeling nonlinear systems using volterra models based on kautz functions the drawback of requiring a large number of parameters in the representation of these models can be circumvented by describing every kernel using an orthonormal basis of functions such as the kautz basis the resulting model so called wiener volterra model can be truncated into a few terms if the kautz functions are properly designed the underlying problem is how to select the free design complex poles that fully parameterize these functions a solution to this problem has been provided in the literature for linear systems which can be represented by first order volterra models a generalization of such strategy focusing on volterra models of any order is presented in this paper this problem is solved by minimizing an upper bound for the error resulting from the truncation of the kernel expansion into a finite number of functions the aim is to minimize the number of two parameter kautz functions associated with a given series truncation error thus reducing the complexity of the resulting finite dimensional representation the main result is the derivation of an analytical solution for a sub optimal expansion of the volterra kernels using a set of kautz functions

pertinent choice of parameters for discrete kautz approximation kautz functions have received much attention in the recent mathematical modeling and identification literature these functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior we consider here the choice of the free parameters in discrete two parameter kautz approximation using a key relationship between kautz and laguerre expansions we derive an upper bound for the quadratic truncation error minimization of this upper bound yields pertinent parameters whose computation then requires reduced knowledge of the function to be modeled

optimality conditions for truncated kautz networks with two periodically repeating complex conjugate poles presents optimality conditions for the approximation of a siso system by a truncated kautz network with two repeating complex conjugate poles both the continuous and the discrete time cases are discussed the author approaches the problem in a system approximation framework and he does not assume that the input signal is white or an impulse the results obtained generalize the results already known for truncated laguerre networks

iterated filter banks with rational rate changes connection with discrete wavelet transforms some properties of two band filter banks with rational rate changes rational filter banks are first reviewed focusing then on iterated rational filter banks compactly supported limit functions are obtained in the same manner as previously done for dyadic schemes allowing a characterization of such filter banks these functions are carefully studied and the properties they share with the dyadic case are highlighted they are experimentally observed to verify a shift property strictly verified in the dyadic ease up to an error which can be made arbitrarily small when their regularity increases in this case the high pass outputs of an iterated filter bank can be very close to samples of a discrete wavelet transform with the same rational dilation factor straightforward extension of the formalism of multiresolution analysis is also made finally it is shown that if one is ready to put up with the loss of the shift property rational iterated filter banks can be used in the same manner as if they were dyadic filter banks with the advantage that rational dilation factors can be chosen closer to 1

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

on the determination of the optimal pole position of laguerre filters as is known in the literature at each stationary point of the squared error se curve of a laguerre filter at least one of a pair of certain laguerre coefficients weights vanishes the author describes a very efficient way to compute the derivatives of each one of these coefficients with respect to the pole position of the laguerre filter the knowledge of these derivatives makes possible the computation of high order approximations to the coefficients in question such as truncated taylor series and pade approximants the zeros of these approximations are usually good estimates of the location of the stationary points of the se curve nearer to the center of the approximation in this way the position of these stationary points in particular local minima can be estimated without resorting to a numerical search algorithm both continuous time and discrete time laguerre filters are discussed excited either by an impulse or by an arbitrary signal the authors illustrate the main results of the paper with a numerical example

comb and multiplexed wavelet transforms and their applications to signal processing as an extension of wavelet theory new wavelet bases that are discrete in nature and suitable for the analysis and synthesis of pseudo periodic digital signals are introduced by means of these bases the signal is represented in terms of a periodic trend and aperiodic fluctuations at several scales in the frequency domain the periodic trend lies in bands that are centered on the harmonics while the fluctuations are distributed in several sidebands properties of comb and multiplexed wavelet transforms are examined and the concepts applied to the analysis of real life signals in one dimension the new transforms have interesting applications to speech and music signal processing their extension to two dimensions may be useful for the analysis of pseudo periodic images

laguerre gram reduced order modeling we present an efficient model reduction procedure based on the laguerre description of the system to be approximated using a one order operator defined in the laplace domain we construct a pencil of functions and formulate the problem as the minimization of the l sub spl infin sup 2 spl ropf sup criterion the use of a weight function in the inner product definition allows a control of the time error spreading in model reduction procedure we show how the required gram matrix can be computed efficiently and prove that the impulse response of the reduced model is also in l sub spl infin sup 2 spl ropf sup the transfer function approach allows an immediate and promising application in model reduction of infinite dimensional systems an extension to multiple input multiple output systems is also given

resultants and chow forms via exterior syzygies let w be a vector space of dimension n 1 over a field k the chow divisor of a k dimensional variety x in p p w is the hypersurface in the grassmannian gk 1 of planes of codimension k 1 in p whose points over the algebraic closure of k are the planes that meet x the chow form of x is the defining equation of the chow divisor for example the resultant of k 1 forms of degree e in k 1 variables is the chow form of p embedded by the e th veronese mapping in p with n k e k 1 more generally the chow divisor of a k cycle i ni vi on projective space is defined to be i nidi where di is the chow divisor of vi the chow divisor of a sheaf f with k dimensional support is the chow divisor of the associated k cycle of f in this paper we will give a new expression for the chow divisor and apply it to give explicit formulas in many new cases starting with a sheaf f on p we use exterior algebra methods to define a canonical and effectively computable chow complex of f on each grassmannian of planes in p if f has k dimensional support we show that the chow form of f is the determinant of the chow complex of f on the grassmannian of planes of codimension k 1 the beilinson monad of f beilinson 1978 is the chow complex of f on the grassmannian of 0 planes that is on p itself in particular we are able to give explicit determinantal and pfaffian formulas for resultants in some cases where no polynomial formulas were known for example the horrocks mumford bundle gives rise to polynomial formulas for the resultant of five homogeneous forms of degrees 4 6 or 8 in five variables the easiest of our new formulas to write down is for the resultant of 3 quadratic forms in three variables the chow form of the veronese surface in p using the tangent bundle of p conclude that it can be written in bezout form described below as the pfaffian of the matrix 0 245 345 135 045 035 145 235

optimal free parameters in orthonormal approximations we consider orthonormal expansions where the basis functions are governed by some free parameters if the basis functions adhere to a certain differential or difference equation then an expression can be given for a specific enforced convergence rate criterion as well as an upper bound for the quadratic truncation error this expression is a function of the free parameters and some simple signal measurements restrictions on the differential or difference equation that make this possible are given minimization of either the upper bound or the enforced convergence criterion as a function of the free parameters yields the same optimal parameters which are of a simple form this method is applied to several continuous time and discrete time orthonormal expansions that are all related to classical orthogonal polynomials

fast computation of frequency warping transforms in this paper we introduce an analytical approach for the frequency warping transform criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined such operators can be used to shape the tiling of time frequency tf plane in a flexible way moreover they are designed to be inverted by the application of their adjoint operator according to the proposed model the frequency warping transform is computed by considering two additive operators the first one represents its nonuniform fourier transform approximation and the second one suppresses aliasing the first operator is fast computable by various interpolation approaches a factorization of the second operator is found for arbitrary shaped nonsmooth warping maps by properly truncating the operators involved in the factorization the computation turns out to be fast without compromising accuracy

online optimization of the time scale in adaptive laguerre based filters a new online method to optimize the free parameter in adaptive laguerre based filters is presented it is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error the proposed technique presents a fast convergence and a good robustness

an optimum time scale for discrete laguerre network any discrete time stable transfer function can be expressed by a discrete time laguerre series with a chosen time scale an optimum time scale such that an index is minimized is derived this index ensures that the coefficients of higher order laguerre functions go toward zero quickly the solution derived requires the knowledge of the impulse response of the discrete plant cases of first order plants second order underdamped plants and plants with multiunit delay are also discussed

sampling rate reduction in multichannel processing of bandpass signals the uniform sampling rate required to reconstruct a deterministic bandpass signal x t having spectrum confined to i1 i2 where i1 0 2 0 2 i2 0 2 0 2 with 0 2 0 depends critically on the positioning of the band and varies from to 2 samples per second the minimum rate of being attained if and only if 0 2 is an integer multiple of if the bandpass signal x is now used as a common input to an even number m of linear time invariant filters to produce m outputs z1 t zm t then it is proved that under a certain independence requirement on the filters a matrix function condition the input x may be reconstructed from samples of the outputs zk t each output being sampled at the uniform rate of m samples second or 1 m th the minimum sampling rate associated with the input the dependence on band position is removed by a partitioning of the set i1 i2 into m disjoint subsets j1 jm of equal length and a subsequent mapping procedure which allows j1

brief optimal expansions of discrete time volterra models using laguerre functions this work is concerned with the optimization of laguerre bases for the orthonormal series expansion of discrete time volterra models the aim is to minimize the number of laguerre functions associated with a given series truncation error thus reducing the complexity of the resulting finite dimensional representation fu and dumont ieee trans automatic control 38 6 1993 934 indirectly approached this problem in the context of linear systems by minimizing an upper bound for the error resulting from the truncated laguerre expansion of impulse response models which are equivalent to first order volterra models a generalization of the work mentioned above focusing on volterra models of any order is presented in this paper the main result is the derivation of analytic strict global solutions for the optimal expansion of the volterra kernels either using an independent laguerre basis for each kernel or using a common basis for all the kernels

application of infinite dimensional linear programming to iir filter design with time domain constraints previously developed infinite dimensional linear programming techniques are used for the design of recursive filters with complex chebyshev error criteria and time domain constraints the approach is applied to a numerical example that deals with the design of a laguerre network as an equalization filter for a digital transmission channel

optimum choice of free parameter in orthonormal approximations this correspondence investigates the choice of a free parameter usually related to time scale that minimizes the error energy when approximating a given signal with some widely used orthonormal basis functions the proposed solution is the best that can be achieved with the limited required knowledge of the signal it is appealing for experimental data for which no exact mathematical expression is available

parametric least squares approximation using gamma bases we study the problem of linear approximation of a signal using the parametric gamma bases in l sup 2 space these bases have a time scale parameter which has the effect of modifying the relative angle between the signal and the projection space thereby yielding an extra degree of freedom in the approximation gamma bases have a simple analog implementation that is a cascade of identical lowpass filters we derive the normal equation for the optimum value of the time scale parameter and decouple it from that of the basis weights using statistical signal processing tools we further develop a numerical method for estimating the optimum time scale