on variable bandwidth selection in local polynomial regression the performances of data driven bandwidth selection procedures in local polynomial regression are investigated by using asymptotic methods and simulation the bandwidth selection procedures considered are based on minimizing prelimit approximations to the conditional mean squared error mse when the mse is considered as a function of the bandwidth h we first consider approximations to the mse that are based on taylor expansions around h 0 of the bias part of the mse these approximations lead to estimators of the mse that are accurate only for small bandwidths h we also consider a bias estimator which instead of using small h approximations to bias naively estimates bias as the difference of two local polynomial estimators of different order and we show that this estimator performs well only for moderate to large h we next define a hybrid bias estimator which equals the taylor expansion based estimator for small h and the difference estimator for moderate to large h we find that the mse estimator based on this hybrid bias estimator leads to a bandwidth selection procedure with good asymptotic and for our monte carlo examples finite sample properties

stochastic theory of continuous time state space identification this paper presents theory algorithms and validation results for system identification of continuous time state space models from finite input output sequences the algorithms developed are methods of subspace model identification and stochastic realization adapted to the continuous time context the resulting model can be decomposed into an input output model and a stochastic innovations model using the riccati equation we have designed a procedure to provide a reduced order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem

identification with stochastic sampling time jitter this work investigates how stochastic sampling jitter noise affects the result of system identification and proposes a modification of known approaches to mitigate the effects of sampling jitter when the jitter is unknown and not directly measurable by just assuming conventional additive measurement noise the analysis shows that the identified model will get a bias in the transfer function amplitude that increases for higher frequencies a frequency domain approach with a continuous time model allows an analysis framework for sampling jitter noise the bias and covariance in the frequency domain model are derived these are used in bias compensated weighted least squares algorithms and by asymptotic arguments this leads to a maximum likelihood algorithm continuous time output error models are used for numerical illustrations

identification of continuous time models the paper considers the problem of estimation of the transfer function of a continuous time dynamic system in the presence of colored noise the author introduces an operator transformation that allows for keeping a continuous time parametrization whereas the parameter estimation can be made by means of a discrete time maximum likelihood algorithm a comparison is made between the performance of the new method in comparison with a standard identification of an armax model the method is useful in cases where it is important to estimate the coefficients of a continuous time transfer function and where it is important to maintain a physical interpretation of the transfer function results

a sampling theory approach for continuous arma identification the problem of estimating continuous domain autoregressive moving average processes from sampled data is considered the proposed approach incorporates the sampling process into the problem formulation while introducing exponential models for both the continuous and the sampled processes we derive an exact evaluation of the discrete domain power spectrum using exponential b splines and further suggest an estimation approach that is based on digitally filtering the available data the proposed functional which is related to whittle s likelihood function exhibits several local minima that originate from aliasing the global minimum however corresponds to a maximum likelihood estimator regardless of the sampling step experimental results indicate that the proposed approach closely follows the cramer rao bound for various aliasing configurations

power law shot noise the behavior of power law shot noise for which the associated impulse response functions assume a decaying power law form is explored expressions are obtained for the moments moment generating functions amplitude probability density functions autocorrelation functions and power spectral densities for a variety of parameters of the process for certain parameters the power spectral density exhibits 1 f type behavior over a substantial range of frequencies so that the process serves as a source of 1 f sup alpha shot noise for alpha in the range 0

modified euler frobenius polynomials with application to sampled data modelling the broad class of polynomials generally known as eulerian or euler frobenius polynomials has a rich history in mathematics and engineering they have been generalised in several directions and find application in diverse areas ranging from sampled data modelling and polynomial interpolation to wavelets here we describe a modified class of euler frobenius polynomials which are functions of two independent variables we show that the sampling zero dynamics of general linear and nonlinear systems can be described using this new class of polynomials when considering several non standard sampled data modelling problems including when generalised hold functions are used to generate the input and when the continuous system has a time delay

offset dpsk and a comparison of conventional and symmetric dpsk with noise correlation and power imbalance the bit error rate performance of binary dpsk with an arbitrary offset of the phase change vector is derived in the presence of noise correlation and power imbalance and the special cases of conventional dpsk 0 phase change offset and symmetric dpsk pi 2 phase change offset are compared precise conditions are given for optimum offsets and it is shown that from a practical standpoint conventional dpsk gives the optimum performance of any offset scheme and outperforms symmetric dpsk by an order of magnitude and more in error rate when the noise correlation becomes significant it is also found that performance improvement over conventional dpsk can be realized provided the noise correlation is known by making the bit decision regions in phase space unequal thereby demonstrating that the map estimator for dpsk without correlation is no longer optimum when the noise is correlated

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

on m ary dpsk transmission over terrestrial and satellite channels the error rate performance of m ary dpsk systems is investigated in the presence of phase change offset noise correlation and power imbalance both the terrestrial channel and the hard limiting satellite repeater channel are considered in the satellite repeater case the noise correlations and power imbalances are assumed to be present on both the up and downlinks the emphasis is on exact results or asymptotic approximations obtained therefrom as opposed to error rate bounds most of the results are given in terms of integrals readily evaluated by quadrature performance curves showing the effects of the various impairments are presented some specific conclusions which follow from the results are that 1 the phase change offset is relatively unimportant for m geq 4 2 the m ary case is less sensitive to imbalance than is the binary case and 3 the satellite link performance depends strongly upon the quality of the uplink

series representations for rice s ie function two new series representations for the rice function ie k x are presented one of the series involves the modified struve functions and the other involves the modified bessel functions these two series complement each other in their convergence speeds as functions of the values of k and x the truncation error bounds are derived for both series therefore they can be used alternatively with high efficiency and known precision

brief paper stochastic system transformation using generalized orthonormal basis functions with applications to continuous time system identification this paper studies the system transformation using generalized orthonormal basis functions that include the laguerre basis as a special case the transformation of the deterministic systems is studied in the literature which is called the hambo transform the aim of the paper is to develop a transformation theory for stochastic systems the paper establishes the equivalence of continuous and transformed discrete time stochastic systems in terms of solutions the method is applied to the continuous time system identification problem it is shown that using the transformed signals the po moesp subspace identification algorithm yields consistent estimates for system matrices an example is included to illustrate the efficacy of the proposed identification method and to make a comparison with the method using the laguerre filter

on the unique identification of continuous time autoregressive models from sampled data in this work we investigate the relationship between continuous time autoregressive ar models and their sampled version we consider uniform sampling and derive criteria for uniquely determining the continuous time parameters from sampled data the model order is assumed to be known we achieve this by removing a set of measure zero from the collection of all ar models and by investigating the asymptotic behavior of the remaining set of autocorrelation functions we provide necessary and sufficient conditions for uniqueness of general ar models and we demonstrate the usefulness of this result by considering particular examples we further exploit our theory and introduce an estimation algorithm that recovers continuous time ar parameters from sampled data regardless of the sampling interval we demonstrate the usefulness of our algorithm for various gaussian and non gaussian ar processes

frequency domain system identification using arbitrary signals it is the common conviction that frequency domain system identification suffers from the drawback that it cannot handle arbitrary signals without introducing systematic errors this paper shows that it is possible to deal with nonperiodic signals without any approximation and under the same assumptions as in the time domain by estimating simultaneously some initial conditions and the system model parameters

computing stochastic continuous time models from arma models some algorithms for computing the underlying continuous time stochastic model from a sampled arma model are presented three algorithms are given all having a modest computational complexity the properties of the algorithms are analysed and also illustrated by means of numerical examples

batch scheme recursive parameter estimation of continuous time systems using the modulating functions method abstract the modulating functions method is a very effective method for parameter estimation of continuous time systems that are linear in their parameters one efficient implementation developed by pearson and lee involves the use of trigonometric functions and fast computations offered by fpt techniques in this paper a recursive implementation of the method is developed for on line parameter estimation of a continuous time system by shifting a fixed window of time series data one step forward at each sampling instant the resulting recursion algorithms are fast and use the identities of discrete fourier transforms along with some inherent commutative properties a simulation example with a van der pol oscillator is included to investigate the performance of the proposed estimation method

comparison of interpolating methods for image resampling when resampling an image to a new set of coordinates for example when rotating an image there is often a noticeable loss in image quality to preserve image quality the interpolating function used for the resampling should be an ideal low pass filter to determine which limited extent convolving functions would provide the best interpolation five functions were compared a nearest neighbor b linear c cubic b spline d high resolution cubic spline with edge enhancement a 1 and e high resolution cubic spline a 0 5 the functions which extend over four picture elements c d e were shown to have a better frequency response than those which extend over one a or two b pixels the nearest neighbor function shifted the image up to one half a pixel linear and cubic b spline interpolation tended to smooth the image the best response was obtained with the high resolution cubic spline functions the location of the resampled points with respect to the initial coordinate system has a dramatic effect on the response of the sampled interpolating function the data are exactly reproduced when the points are aligned and the response has the most smoothing when the resampled points are equidistant from the original coordinate points thus at the expense of some increase in computing time image quality can be improved by resampled using the high resolution cubic spline function as compared to the nearest neighbor linear or cubic b spline functions

banach spaces related to integrable group representations and their atomic decompositions i abstract we present a general theory of banach spaces which are invariant under the action of an integrable group representation and give their atomic decompositions with respect to coherent states i e the atoms arise from a single element under the group action several well known decomposition theories are contained as special examples and are unified under the aspect of group theory

brief paper on the indirect approaches for carma model identification in this paper we study the problem of reconstructing a continuous time ct model from an identified discrete time dt model for a continuous time stochastic process we present a new necessary and sufficient condition for the existence of the solution we also show that the solution is unique if it exists our results are useful in modeling multivariable processes as well these results are then used to develop an algorithm where the intermediate discrete time model estimation is not necessary the performance of our algorithm is illustrated using numerical simulations

two dimensional spline interpolation for image reconstruction a scheme of two dimensional 2 d spline interpolation for image reconstruction is presented it is aimed to be applied in image data compression an impulse response derived from 2 d quadratic spline functions is theoretically analysed then it is approximated to be a finite duration one fir for practical implementation with this scheme compression rate of greater than 12 is achieved for x ray left ventricular cineangiogram image data compression

subspace identification for continuous time stochastic systems via distribution based approach this paper presents a novel approach for system identification of continuous time stochastic state space models from random input output continuous data the approach is based on the introduction of random distribution theory in describing higher time derivatives of stochastic processes and the input output algebraic relationship is derived which is treated in the time domain the efficacy of the approach is examined by comparing with other approaches employing the filters

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

what is variable bandwidth we propose a new notion of variable bandwidth that is based on the spectral subspaces of an elliptic operator apf ddx p x ddx f where p 0 is a strictly positive function denote by c ap the orthogonal projection of ap corresponding to the spectrum of ap in the range of this projection is the space of functions of variable bandwidth with spectral set in we will develop the basic theory of these function spaces first we derive nonuniform sampling theorems second we prove necessary density conditions in the style of landau roughly for a spectrum 0 the main results say that in a neighborhood of x a function of variable bandwidth behaves like a band limited function with local bandwidth p x 1 2 although the formulation of the results is deceptively similar to the corresponding results for classical band limited functions the methods of proof are much more involved on the one hand we use the oscillation method from sampling theory and frame theoretic methods on the other hand we need the precise spectral theory of sturm liouville operators and the scattering theory of one dimensional schrodinger operators 2017 wiley periodicals inc

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

the effects of rapid sampling in system identification this paper deals with the effects of rapid sampling in system identification in continuous time noise models of non zero relative degree imply that one has to differentiate the measured data to find the prediction error parameter estimate this problem can be avoided by using noise models of relative degree zero or by introducing prefilters the corresponding difficulty for the discrete time case is less obvious however by linking the discrete time and continuous time parameter estimation problem we show that the same problem arises for rapid sampled systems

improved finite word length characteristics in digital control using delta operators this paper examines some of the consequences of finite word lengths in digital control it is shown that in many cases of practical importance the usual shift operator formulation is inferior to an alternative formulation which we designate the delta operator approach this latter approach is shown to give better coefficient representation and less roundoff noise in many cases we thus argue that the shift operator and its associated z transform can be replaced by delta operators and their associated transform which we designate a transform an added advantage of this approach is that discrete designs and transforms converge to their continuous time counterparts as the sampling rate is increased

frequency domain identification of continuous time arma models from sampled data the subject of this paper is the direct identification of continuous time autoregressive moving average carma models the topic is viewed from the frequency domain perspective which then turns the reconstruction of the continuous time power spectral density ct psd into a key issue the first part of the paper therefore concerns the approximate estimation of the ct psd from uniformly sampled data under the assumption that the model has a certain relative degree the approach has its point of origin in the frequency domain whittle likelihood estimator the discrete or continuous time spectral densities are estimated from equidistant samples of the output for low sampling rates the discrete time spectral density is modeled directly by its continuous time spectral density using the poisson summation formula in the case of rapid sampling the continuous time spectral density is estimated directly by modifying its discrete time counterpart

on the relationship between spline interpolation sampling zeros and numerical integration in sampled data models abstract real systems are usually modeled in continuous time by differential equations in practice however we have to deal with them using discretized models and sampled data these models however have more zeros than the continuous time model in this paper we show that there is a specific relation between these sampling zeros and the smoothness of the continuous time input to the plant generated by a hold device using spline interpolation on the other hand in numerical analysis ordinary differential equations are solved using numerical integration methods such as runge kutta in this paper we also characterize the asymptotic sampling zeros of approximate sampled data models when using a runge kutta method of a given order under uniform sampling and the input signal is obtained by spline interpolation these results show the strong connections between the presence and characterization of sampling zeros spline interpolation and numerical integration techniques moreover the results presented in the paper provide additional insights about the impact of the details of the sampling process on the resulting discrete time model

numerical integration approach to on line identification of continuous time systems abstract the problem of estimating the parameters in linear continuous differential equation models from sampled data is treated using a linear integral filter we can obtain an identification model that is parametrized directly in the continuous time model parameters the unknown initial states of the system do not require estimation the choice of the sampling interval and the design of the linear integral filter are discussed considering the accuracy of parameter estimates and the computational burden by applying the results from discrete time model identification with the obtained identification model a discrete time parameter estimation method is developed and the necessary condition as well as the sufficient condition on the input for consistency are explicitly derived and discussed in particular situations a simulation study is also included to confirm the theoretical results

the effects of noise correlation and power imbalance on terrestrial and satellite dpsk channels new results are given for the bit error probability for binary dpsk modulation over both terrestrial and satellite channels taking into account noise correlation and power imbalance the new expressions are remarkably simpler than their previously published counterparts for the terrestrial channel the results are in closed form in terms of tabulated functions and for the hard limiting satellite channel both in terms of integrals readily evaluated by quadrature and in terms of infinite series using the results it is shown that the error rate does not depend on the noise correlation down link in the satellite case so long as the a priori symbol probabilities are equal thereby solving an open problem posed by lee french and hong also the satellite case in which each of the up link and down link channels contains nonzero noise correlations is briefly treated

on zero locations for sampled stochastic systems zero locations of stochastic models have significant influence on optimal prediction algorithms as well as on the convergence speed of identification method the possible zero locations for a sampled stochastic system are examined in particular it is shown and numerically illustrated that the sampled zeros can appear only in a restricted set within the unit circle a complete analysis of second order systems is given and all possible zero locations are characterized it is shown how the zero location in this case depends on the continuous time model parameters and the sampling interval

brief parameter identification with derivative shift operator parametrization a way of parametrizing linear systems using an operator which combines the two commonly used operators the shift q and the delta d operators is proposed it is shown that the proposed parametrization improves the numerical property of parameter identification process by using the proposed operator the condition number of the information matrix in the identification algorithm is significantly lower than that using the q or d operator it is also shown that accurate and fast converging parameter identification can be achieved by using the new operator at fast sampling rates especially for systems with relatively wide bandwidth the numerical superiority of the new parametrization is demonstrated by simulation results

on differential detection of m ary dpsk with intersymbol interference and noise correlation in this paper we study differential detection of m ary differential phase shift keyed dpsk signals with intersymbol interference and noise correlation with these impairments there can be a wide variation in the error rate of the individual symbols with this variation increasing with m however by adding a phase shift offset and adjusting the decision boundaries in the detector this variation can be reduced and the average symbol error rate can be decreased for example for quaternary dpsk with a signal to adjacent from the previous and next symbols intersymbol interference power ratio of 17 db these methods can reduce the variation in symbol error rates by more than two orders of magnitude and decrease the required signal to thermal noise ratio for a 10 6symbol error rate by more than 2 db

identification of continuous time systems using arbitrary signals abstract this paper presents a parametric frequencydomain identification algorithm for linear time invariant continuous time systems excited by arbitrary signals unlike the current available methods this approach allows accurate modeling in the complete frequency band from dc to nyquist

limit results for sampled systems properties of discrete time systems obtained by sampling continuous time systems are described by introducing prefilters we can treat different ways of sampling within one framework results on the convergence of poles and zeros of transfer functions and noise filters as the sampling interval tends to zero are given these results are generalizations of the results of astrom hagander and sternby 1984 on the convergence of poles and zeros for zero order hold sampled transfer functions sampled noise models are also analysed knowledge of these properties is very important in for example discrete time simulations of continuous time systems and identification of continuous time models based on discrete time measurements

brief performance evaluation of methods for identifying continuous time autoregressive processes identification of continuous time autoregressive processes from discrete time data by replacing the differentiation operator by an approximation is considered a linear regression model can then be formulated the least squares method and the instrumental variables method must be used with some care to get parameter estimates of good quality the bias is studied explicitly in the paper together with the asymptotic distribution and expressions are presented for the covariance matrix of the estimated parameters it turns out that there are small differences in the dominating bias term for the different methods whereas the statistical properties are comparable overall the performance is similar to that of a prediction error method for short sampling intervals

brief identification of continuous time ar processes from unevenly sampled data when identifying a continuous time ar process from discrete time data an obvious approach is to replace the derivative operator in the continuous time model by an approximation in some cases a linear regression model can then be formulated the well known least squares method would be very desirable to apply since it enjoy good numerical properties and low computational complexity in particular for fast or nonuniform sampling the focus of this paper is the latter i e nonuniform sampling two consistent least squares schemes for the case of unevenly sampled data are presented the precise choice of derivative approximation turns out to be crucial the obtained results are compared to a prediction error method

relative zero location for second order sampled systems it is shown that the pole zero configuration of relevant families of second order continuous time transfer functions is preserved after sampling the results are valid for any sampling period and give tighter bounds for the location of the sample zero than those reported in earlier literature these results complement the analysis made by t soderstrom ibid vol 35 p 1249 53 1990 on the zero location of second order sampled systems

sampled data models for nonlinear stochastic systems truncation errors and sampling zero dynamics in this paper we consider nonlinear stochastic systems and intersect ideas from nonlinear control theory and numerical analysis in particular we use the idea of relative degree this concept guarantees smoothness properties of the output and this in turn allows one to establish properties that are unique to the control theoretic perspective the contributions of the current paper are threefold firstly we define different error measures that extend the ideas of local and global approximation errors for nonlinear stochastic systems secondly we demonstrate that the concept of relative degree plays a key role in obtaining higher order of accuracy for integration procedures compared to euler maruyama integration we show that a particular state space model named stts model has an improved order of accuracy when compared to an euler maruyama approximation at no significant extra computational cost thirdly we show that a further approximation to the stts model named mstts model while retaining the order of local errors has explicit sampling zero dynamics associated with the noise processes that have no continuous time counterpart the extra zero dynamics are shown to be a function of the euler frobenius polynomials to the best of the authors knowledge this is the first reference to sampling zero dynamics for stochastic nonlinear systems

time series analysis in the frequency domain this correspondence presents a parametric frequency domain identification algorithm for autoregressive moving average arma processes that does not suffer from spectral leakage errors it is based on an extended transfer function model that takes into account the begin and end effect of the finite data record the relationship with the one step ahead prediction error method is established the advantages of the proposed method are easy prefiltering and leakage free spectral representation of the raw data

fast b spline transforms for continuous image representation and interpolation efficient algorithms for the continuous representation of a discrete signal in terms of b splines direct b spline transform and for interpolative signal reconstruction indirect b spline transform with an expansion factor m are described expressions for the z transforms of the sampled b spline functions are determined and a convolution property of these kernels is established it is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering fast computational algorithms based on the recursive implementations of these filters are proposed a b spline interpolator can also be characterized in terms of its transfer function and its global impulse response cardinal spline of order n the case of the cubic spline is treated in greater detail the present approach is compared with previous methods that are reexamined from a critical point of view it is concluded that b spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

brief paper generalized sampled data hold functions with asymptotic zero order hold behavior and polynomic reconstruction we present a generalized sampled data hold function that combines arbitrary z domain zero placement ability with zero order hold behavior under constant input thus exhibiting minimal intersample ripple by design our hold can be regarded as a generalization of the fractional order hold with a polynomial instead of a simple linear pattern and therefore with as many tuning parameters as desired moreover the polynomial approach turns out to provide a simple mechanism of control energy minimization among other benefits all these features help to achieve qualitatively better perfect model referencing because problematic sampling z zeros or the intersample issues of the conventional generalized holds need no longer be endured

on sampled data models for nonlinear systems models for deterministic continuous time nonlinear systems typically take the form of ordinary differential equations to utilize these models in practice invariably requires discretization in this paper we show how an approximate sampled data model can be obtained for deterministic nonlinear systems such that the local truncation error between the output of this model and the true system is of order spl delta sup r 1 where spl delta is the sampling period and r is the system relative degree the resulting model includes extra zero dynamics which have no counterpart in the underlying continuous time system the ideas presented here generalize well known results for the linear case we also explore the implications of these results in nonlinear system identification

parametric identification of transfer functions in the frequency domain a survey this paper gives a survey of frequency domain identification methods for rational transfer functions in the laplace s or z domain the interrelations between the different approaches are highlighted through a study of the equivalent cost functions the properties of the various estimators are discussed and illustrated by several examples

brief box jenkins continuous time modeling this paper treats the identification of continuous time models using arbitrary band limited excitation signals a modeling approach is presented that has the following two advantages 1 asymptotically the amount of data tends to infinity there is no approximation error over the complete frequency band from dc to nyquist 2 it allows to identify general parametric noise models the key idea is to combine a continuous time plant model with a discrete time noise model hybrid box jenkins model structure

sampling zeros and the euler frobenius polynomials we show that the zeros of sampled data systems resulting from rapid sampling of continuous time systems preceded by a zero order hold zoh are the roots of the euler frobenius polynomials using known properties of these polynomials we prove two conjectures of hagiwara et al 1993 the first of which concerns the simplicity negative realness and interlacing properties of the sampling zeros of zoh and first order hold foh sampled systems to prove the second conjecture we show that in the fast sampling limit and as the continuous time relative degree increases the largest sampling zero for foh sampled systems approaches 1 e where e is the base of the natural logarithm

frequency domain system identification using non parametric noise models estimated from a small number of data sets abstract this paper discusses the problem of identifying a linear system from the frequency data when the measurements of the input and the output signals are both disturbed with noise a typical example of such a problem is the identification of a system in a feedback loop it is known that this problem can be solved using errors in varaibles methods if the covariance matrices of the disturbing noise on input and output measurements are a priori known it is shown that the exact covariance matrices can be replaced by the sample covariance matrices the system can be identified from the sample means and sample covariance matrices calculated from a small number m of independently repeated experiments it is shown that under these conditions the estimates are still strongly consistent for an increasing number of data points n in each experiment n if m 4 the loss in efficiency is quantified m 6 and the expected value of the cost function m 4 and its variance m 6 are calculated

sampling zeros of discrete models for fractional order systems most real systems evolve in continuous time and are modeled using differential equations however discrete time sampled data models are necessary to describe the interaction with digital devices for rational transfer functions with integer order derivatives a well known consequence of the sampling process is the presence of sampling zeros in this note we extend this result to systems described in terms of fractional order derivatives specifically we define fractional order euler frobenius polynomials and we use them to characterize the asymptotic sampling zeros for fractional systems as the sampling period tends to zero

functions of variable bandwidth via time frequency analysis tools abstract this paper is motivated by the apparent lack of a precise mathematical description of the very natural idea of variable bandwidth for a function defined on the real line different existing concepts suffer from serious shortcomings we will present a new and mathematically well justified function space model which is based on the theory of coorbit spaces in a time frequency context making use of the flexibility of this approach we define a family of hilbert spaces which can be viewed as generalised modulation spaces more precisely we define a family of banach spaces of functions with variable bandwidth vb functions by imposing a weighted mixed norm condition on the short time fourier transform of their elements punishing the contributions outside a strip of variable width described by the band width function b similar bandwidth functions define the same space with equivalent norms any good gabor frame e g with schwartz windows can be used to characterize the membership of a function in such a space moreover various classes of functions e g those obtained by a time variant filter are shown to belong to such a space in addition error estimates are given when approximating certain subclasses

frequency domain identification of continuous time output error models part i uniformly sampled data and frequency function approximation this paper treats several aspects relevant to identification of continuous time output error oe models based on sampled data the exact method for doing this is well known both for data given in the time and frequency domains this approach becomes somewhat complex especially for non uniformly sampled data we study various ways to approximate the exact method for reasonably fast sampling while an objective is to gain insights into the non uniform sampling case this paper only gives explicit results for uniform sampling

continuous time identification of siso systems using laguerre functions this paper looks at the problem of estimating the coefficients of a continuous time transfer function given samples of its input and output data we first prove that any nth order continuous time transfer function can be written as a fraction of the form spl sigma sub k 0 sup n b sub k l sub k s spl sigma sub k 0 sup n a sub k l sub k s where l sub k s denotes the continuous time laguerre basis functions based on this model we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps 1 filter both the input and output data by l sub k s and 2 estimate a sub k b sub k and relate them to the coefficients of the transfer function for practical implementation we require the discrete time approximation of l sub k s since only sampled data is available we propose a scheme that is based on higher order pade approximations and we prove that this scheme produces discrete time filters that are approximately orthogonal and consequently a well conditioned numerical problem some other features of this new algorithm include the possibility to implement it as either an off line or a quasi on line algorithm and the incorporation of constraints on the transfer function coefficients a simple example is given to illustrate the properties of the proposed algorithm

function spaces obeying a time varying bandlimit abstract motivated by applications to signal processing and mathematical physics recent work on the concept of time varying bandwidth has produced a class of function spaces which generalize the paley wiener spaces of bandlimited functions any regular simple symmetric linear transformation with deficiency indices 1 1 is naturally represented as multiplication by the independent variable in one of these spaces we explicitly demonstrate the equivalence of this model for such linear transformations to several other functional models based on the theories of meromorphic model spaces of hardy space and purely atomic herglotz measures on the real line respectively this theory provides a precise notion of a time varying or local bandwidth and we describe how it may be applied to construct signal processing techniques that are adapted to signals obeying a time varying bandlimit

an algebraic theory for design of controllers for linear multivariable systems part ii feedback realizations and feedback design the study of general linear multivariable systems with possibly different controlled and measured outputs is continued in this part of the paper the structure matrices defined in part i are used to solve the feedback realization problem feedback realizable transfer functions are then used to solve problems of regulator type it is shown that the solutions to problems like disturbance deeoupling output regulation and pole placement are all special cases of the solution to a more general problem finally it is shown how the results of part i and part ii can be combined to solve problems of servo type and of regulator type simultaneously

on binary dpsk error rates due to noise and intersymbol interference this paper presents a new series for evaluating the conditional bit error rate ber of a given transmitted data sequence in a band limited binary differential phase shift keyed system this series involves modified struve functions and it was found to have converged quickly the conditional ber can then be averaged over all possible bit sequences to yield the system ber the results obtained are close to those reported by g j marshall in our analysis the noise samples a bit period apart were assumed to be uncorrelated