# George E. AntoniouMontclair State University · Department of Computer Science

George E. Antoniou

Ph.D. (NTUA)

## About

113

Publications

9,035

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3,469

Citations

Citations since 2017

Introduction

Additional affiliations

September 1993 - present

## Publications

Publications (113)

This paper introduces generalized circuit and state– space realizations for four–dimensional (4D) ladder structured filters. The proposed 4D circuit realization contains a minimum number of delay elements. In addition the dimension of the state– space vector is minimal. A salient example, simple yet illustrative, of the presented concepts is given.

In this paper a Boolean minimization algorithm is considered and implemented as an applet in Java. The applica-tion is based on the Quine-McCluskey simplification technique with some modifications. The given application can be accessed on line since it is posted on the World Wide Web (WWW), with up to four variables, at the URL http://www.csam.mont...

Adaptive artificial neural network techniques are introduced and applied to the factorization of 2-D second order polynomials. The proposed neural network is trained using a constrained learning algorithm that achieves minimization of the usual mean square error criterion along with simultaneous satisfaction of multiple equality and inequality cons...

An algorithm is presented for minimal state-space realization of two-dimensional (2-D) systems. The method is based on the idea of expanding the transfer function in a 2-D continued fraction. The algorithm proposed in conceptually and computationally simple.

The authors point out that the progress of an epidemic can be
modeled by a mathematical process. In order to apply the required
mathematical control engineering techniques, all the variables of the
mathematical model describing the epidemic process have to be available
from measurements. In the case where a variable or a parameter is not
available...

This research presents a circuit realization for four-dimension (4D) reverberator-based two-input, two-output all-pass structured discrete filters. The proposed 4D circuit realization requires, for its implementation, a minimum number of delay elements. As a result, the dimension of the state-vector, of the derived 4D state space model, is minimal...

This paper proposes generalized circuit and state space realizations for four–dimensional (4D) Finite Impulse Response (FIR) filters. Specifically, lattice and direct-form filter structures are considered. The 4D circuit realizations utilize, for their implementation, a minimum number of delay elements.
Further, the dimensions of the state–space ve...

In this paper a useful educational tool is presented for minimizing low order Boolean expressions. The algorithm follows the Karnaugh map looping approach. For the implementation, which provides optimal results, C++ coding was used on the Embedded Visual C++ 3.0 Pocket PC using Windows CE Operating System environment. In order to make the overall i...

The problem of minimal state space realization of two-dimensional systems is considered. The approach followed is, initially, to derive a circuit realization of the given transfer function involving a minimum number of delay elements. To facilitate this realization, the transfer function is expanded into a continued fraction. Using this circuit rea...

This paper presents a circuit realization for four– dimensional (4D) lattice discrete filters. The proposed 4D circuit realization requires, for its implementation, a minimum number of delay elements. Further, the dimension of the state-vector, of the derived 4D state space model, is minimal and its 4D transfer function is characterized by the all–...

In this paper state space and circuit realizations are presented for 2D Reverse-Lattice based filters. The proposed state space realizations are based on the corresponding circuit implementation. For the state space realization the 2D Cyclic model, having minimal dimension and delay elements, is used. Two low-order representative examples are prese...

In this paper the classical and generalized numerical Rogers–Ramanujan continued fractions are extended to a polynomial continued fraction in one and two dimensions. Using the new continued fractions, the fundamental recurrence formulas and a fast algorithm, based on matrix formulations, are given for the computation of their transfer functions. Th...

In this paper a two-dimensional (2D) minimal circuit and state space realization is presented for a 2D continued fraction expansion of Roger-Ramanujan type. The proposed state space realization is based on the corresponding circuit implementation. For the state-space realization the 2D Roesser model of cycled structure is used. The dimension of the...

In this paper two dimensional (2D) minimal circuit and state space realizations are presented for 2D all-pole systems with coefficient symmetry. The proposed state space realization is based on the corresponding circuit implementation. For the state space realization the classical 2D model of the Roesser type is used. The dimension of the state vec...

In this paper 2-D circuit and state space realizations are presented for FIR bidiagonal discrete 2-D filters/systems. The proposed state space realization is based on the corresponding circuit implementation. For the state space realization the classical 2-D model of the Roesser type was used. The dimension of the state vector and the number of del...

In this paper the generalized numerical Rogers-Ramanujan continued fraction expansion is extended to two-dimensions (2-D). A new fast algorithm is proposed for the inversion of the 2-D Rogers-Ramanujan continued fraction expansion. The algorithm is based on matrix formulations. The simplicity and efficiency of the algorithm are illustrated by step-...

In this paper state space and circuit realizations are presented for tridiagonal discrete state space 2D filters. The proposed state space realizations are based on the corresponding circuit implementations. For the state space realization the 2D Roesser and Cyclic models are used. The dimension of the state vectors are minimal for both models. A l...

In this paper a circuit realization is presented for generalized three-dimensional (3D) lattice discrete systems/filters. The proposed structure has minimum number of delay elements. Based on this circuit realization the corresponding state space realization-representation is derived. The dimension of the 3D state space vector is minimal and the co...

In this paper, the discrete Fourier transform is used to determine the coefficients of a transfer function of a new generalized two-dimensional system of second-order: Ex(i1 + 2, i2 + 2) = A0x(i1 + 1, i2 + 1) + A1x(i1 + 1, i2) + A2x(i1, i2 + 1). The algorithm is straightforward and has been implemented using the software package Matlab™. A step-by-...

The discrete Fourier transform is used to determine the coefficients of a transfer function for n-order linear systems: . The algorithm is fast, straight forward and easily can be implemented. Two step-by-step examples, illustrating the application of the algorithm, are presented.

A new n-dimensional (multi-dimensional) k-order (multi-order) system-model is introduced as an extension of the corresponding Fornasini-Marchesini model. In addition, using this model the discrete Fourier transform (DFT) is used to determine the coefficients of the transfer function. The DFT-based algorithm is straight forward and can easily be imp...

A new generalized multi-dimensional (n-dimensional) multi-order (k-order) (GnDkO) linear system/model is introduced. Using this model, the discrete Fourier transform (DFT) is used to compute the coefficients of the transfer function. The algorithm is straightforward and can be easily implemented. A step-by-step example illustrating the application...

In this paper, the one-dimensional Gray–Markel lattice-ladder discrete filter structure is extended to two dimensions (2D). The proposed 2D circuit implementation has minimal number of unit delays. Based on this circuit implementation the corresponding 2D state space realization is derived. The matrices A, b, c′ and the scalar d of the 2D state spa...

In this paper the discrete Fourier transform is used to determine the coefficients of a transfer function of a new two-dimensional system model of second-order: x(i<sub>1</sub> + 2, i<sub>2</sub> + 2) = A<sub>0</sub>x(i<sub>1</sub> + 1, i<sub>2</sub> + 1) + A<sub>1</sub>x(i<sub>1</sub> + 1, i<sub>2</sub>) + A<sub>2</sub>x(i<sub>1</sub>, i<sub>2</su...

In this paper a useful educational tool is presented for minimizing low order Boolean expressions. The algorithm follows the Karnaugh map looping approach and provides optimal results. For the implementation, C++ was used on the CodeWarrior for Palm Operating System environment. In order to make the overall implementation efficient, the object orie...

n this paper the discrete Fourier transform (DFT) is used for determining the transfer function coefficients for second-order linear systems:. The proposed algorithm is theoretically attractive, practically fast and has been implemented in Matlab. Two step-by-step examples illustrating the application of the algorithm are given.

In this paper a new approach is presented for the approximate separation of two-dimensional all-zero polynomials. The proposed technique is based on the genetic search algorithm. The implemented genetic algorithm computes the approximate one-dimensional coefficients, the absolute error and useful parameters of the genetic algorithm, using the softw...

The discrete Fourier transform (DFT) is used for determining the coefficients of a transfer function for n-order singular linear systems, Ex (n) = Σi=1n Aix (n+1) + Bu, where E may be singular. The algorithm is straight forward and easily can be implemented. Three step-by-step examples illustrating the application of the algorithm are presented.

In this paper a circuit realization is presented for three-dimensional (3-D) lattice discrete systems/filters. The proposed structure has minimun mumber of delay elements and multipliers. Based on this circuit realization the corresponding state space realization-representation is derived. The dimension of the 3-D state space vector is minimal and...

A theoretically interesting technique is proposed for the determination of the coefficients of the determinantal polynomial and the coefficients of the adjoint polynomial matrix of a given n-D system, described by the Fornasini-Marchesini state space model. The proposed algorithms are based on the discrete Fourier transform (DFT), and easily can be...

In this paper state space realizations for all-pole and all-zero two-dimensional (2D) lattice discrete ®lters are presented. The proposed realizations are based on the corre-sponding circuit implementations . For the realizations, the 2D state space model of the Roesser type was used. The dimension of the state vector was minimal. Three low-order e...

A circuit realization is presented for generalized one-multiplier
lattice discrete two-dimensional (2-D) filters. The proposed structure
has a minimum number of delay elements and multipliers. Based on this
circuit realization, the corresponding state-space
realization-representation is derived. The dimension of the 2-D
state-space vector is minima...

A circuit realization is presented for two-dimensional (2-D) lattice discrete filters. The number of delay elements is minimal. Based on this circuit realization, the corresponding state space realization is derived. The matrices A, b, c', and the scalar d of the 2-D state space model are presented in generalized form. The dimension of the 2-D stat...

A new algorithm is presented for the determination of the coefficients of an n-dimensional (n-D) transfer function. The n-D state-space system is described by the n-D Fornasini–Marchesini models. The proposed algorithm is theoretically attractive and computationally fast and it is based on the discrete Fourier transform (DFT). A step-by-step exampl...

A review on the minimal state space realizations for a clews of N-Dimensional (N-D) discrete - time lossless bounded real functions is presented. Initially the minimal representation is derived from the circuit representation which in fact has minimum number of delay elements and is a particular form of N-D lattice filters. The corresponding transf...

A new computationally fast algorithm is presented for the determination of the coefficients of the determinantal polynomial and the coefficients of the adjoint polynomial matrix of a given 3--D state space model. The algorithm is based on the discrete Fourier transform (DFT) and can be easily implemented on a digital computer.

A theoretically attractive and computationally fast algorithm is presented for the determination of the coefficients of the determinantal polynomial and the coefficients of the adjoint polynomial matrix of a given three-dimensional (3-D) state space model of Fornasini-Marchesini type. The algorithm uses the Discrete Fourier Transform (DFT) and can...

Wavelets have become a popular topic, especially in their use for image compression. Many papers have been written, but most are oriented toward
mathematicians. This paper will present an application of the Daubechies wavelet for image compression with emphasis on the implementation and not on the mathematical analysis.

A circuit realization, for generalized Kelly - Lochbaum discrete two - dimensional (2-D) filters, with minimum number of delay elements is proposed. Using the proposed circuit implementation the corresponding state space realization is derived from its block diagram representation. The dimension of the 2-D state space vector is minimal and the corr...

In this paper two new two--dimensional (2-D) continued fraction expansions, having quadratic structure, are presented. Using their circuit realizations, which in fact are characterized by the minimum number of delay elements, minimal state space representations are derived. The matrices A, b, c of the 2-D state space model are presented in generali...

In this paper the problem of the minimal circuit and state space realization for two-dimensional systems that can be expanded into B-type continued fractions, is considered. The matrix vectors A,b,c', having minimal dimension, and the scalar d of the Givone-Roesser state space model are derived. In addition, the corresponding circuit implementation...

A theoretically attractive and computationally simple algorithm is presented for the determination of the coefficients of the determinantal polynomial and the coefficients of the adjoint polynomial matrix of a given 3-D state space model of Fornasini-Marchesini type. The algorithm uses the discrete Fourier transform (DFT) and can be easily implemen...

A simple technique for state-space realization of 3-dimensional discrete-time lossless bounded real functions is presented. The state-space matrices are of minimal dimension and are derived from the corresponding circuit implementation. The efficiency of the technique is due to the fact that in order to determine the 3D state-space model the circui...

A method is presented for factorizing two-dimensional polynomials,
with the aim of designing 2-D IIR filters in cascade form. A specialized
neural network structure is employed which is a variation of a two-layer
sigma-pi neural network paradigm. By training the network to emulate a
given polynomial, the lower-order factor polynomials are generated...

A method is presented for the factorization of 2D second order
polynomials, based on the application of artificial neural networks
trained by constrained learning techniques. The approach achieves
minimization of the usual mean square error criterion along with
simultaneous satisfaction of constraints between the polynomial
coefficients. Using this...

For a nonlinear process, representing the spread of an epidemic, a neural network is proposed for estimating the rate at which susceptible individuals become infective. The structure of the neural network is simple and the applied adaptive learning law is based on the backpropagation algorithm. The performed simulations verify the good performance...

A technique is proposed for separating a two-dimensional (2-D) polynomial into two one-dimensional (1-D) polynomials.The approach uses the generalized Σ-Π neural network paradigm. By training this uetwork to emulate a given polynomial, the 1-D factor-polynomials are generated. Simulations are performed for sepa.rable and nonseparable 2-D polynomial...

In this paper, the problem of the characteristic polynomial assignment (CPA) for linear shift invariant single-input single-output (SISO) two-dimensional (2-D) systems is considered. Specifically, it is shown that the use of the Fornasini-Marchesini canonical state space model representation facilitates the determination of a feedback control law f...

A circuit realisation for two-dimensional (2D) nth order discrete-time lossless bounded real functions, with minimum number of delay elements, is presented. Based on this circuit realisation the corresponding matrix vectors A, b, c' of the Givone-Roesser 2D state space model, are derived. The dimension of the 2D state space model is minimal.

Abstmct -In this paper, two coupled nonlinear observers are proposed to estimate the equilibrium sugar level as well as the parameter corresponding to the insuline utilizetion characteristics. The equilibrium sugar level varies among individuals, and is typically determined by a medical experiment.....

The problem considered in the paper is the design of a feedback control law such that the closed loop system meets desired performance specifications. Particularly, the authors are dealing with the exact model matching problem for systems with two dimensions, using periodic state and output feedback, assuming that the states and the output are acce...

The problem of minimal state space realization of two-dimensional systems is considered. The approach followed is, initially, to derive a circuit realization of the given transfer function involving a minimum number of delay elements. To facilitate this realization, the transfer function is expanded into a continued fraction. Using this circuit rea...

The transfer function of a full-order compensator for a
single-input, single-output (SISO) linear system designed by the
separation principle is uniquely determined by the locations of the
poles of the closed-loop system and its gain. Hence, the poles of the
observer and of the full-state feedback design can be interchanged
without altering the tra...

A computationally simple algorithm for determining the transfer function of multidimensional singular systems, described by a state-space model based on the Givone-Roesser state space setting, is proposed. The method uses the discrete Fourier transform and can be readily implemented on a digital computer. An example is given to illustrate the simpl...

A simple method is proposed for the factorization of two-dimensional (2- D) polynomials, which makes use of the Sigma-Pi neural network. By training this network to emulate a given polynomial, exact or approximate factors of the polynomials are generated, as appropriate. The algorithm is proven to be accurate and robust when applied in a variety of...

The realization, circuit and state space of two-dimensional (2D) nth order separable all-pass digital filters is considered. The matrices A, b, c′ and the scalar d of the Givone-Roesser state space model are presented in closed form. The dimension of the state space model is minimal. In addition, the corresponding circuit implementation of the filt...

A new method for encoding a videoconference image sequence, termed adaptive neural net vector quantisation (ANNVQ), has been derived. It is based on Kohonen's self-organised feature maps, a neural network type clustering algorithm. The new method differs from it, in that after training the initial codebook, a modified form of adaptation resumes, in...

The problem of the minimal state space realization of two-dimensional transfer functions which are not of any special form such as separable, all pole, all zero, continued fraction expandable, etc. is considered. For this general type of transfer function, an algorithm is presented for the minimal state space realization which is computationally su...

A systematic computer implementable method is proposed for the computation of the transfer function of two-dimensional (2-D) dynamical systems, described by the Fornasini-Marchesini state space model. This technique is based on the Leverrier-Faddeeva algorithm and is conceptually and computationally simple. The algorithm is illustrated by three exa...

A simple method for the computation of the Discrete Fourier Transform (DFT) from the Walsh Transform, using the Neural Network model of Hopfield and Tank, is presented. The proposed method circumvents the algorithmic complexity of the DFT. The computation time for the evaluation of the DFT coefficients depends upon a time constant which characteriz...

The problem of model reduction of three-dimensional systems is studied via orthogonal series. The algorithm proposed reduces the problem to that of solving an overdetermined linear algebraic system of equations, which may readily be solved to yield the simplified model. This model, when approximates adequately the original system, has many importan...

A simple method is presented for the minimal state space realization of two dimensional (2-D) filters, with a three-term separable denominator (3TSD) made up of two 1-D and one 2-D terms. The matrix A and the vectors b and c of the state space model are derived explicitly from the coefficients of the initial transfer function. The circuit implement...

The problem of the circuit and state-space realization of first-
and second-order two-dimensional (2-D) all-pass digital filters is
considered. The method uses the 2-D bilinear transform. The multipliers
and delay elements required for the realization equal the maximum number
of the numerator or denominator coefficients of the given filter. The
mat...

A systematic and conceptually simple algorithm is presented for
the determination of the transfer function for two-dimensional
generalised or singular systems. The method uses the discrete Fourier
transform (DFT) and can easily be applied. The simplicity and efficiency
of the algorithm are illustrated by two examples

A conceptually and computationally simple method is presented for the determination of the minimal state space realization of N-dimensional (N-D) systems. Application of this method requires that the given N-D system, described by its transfer function, can be expanded into a continued fraction. The ease of the method is illustrated by two examples...

In this article, the problem of model reduction of 2-D systems is studied via orthogonal series. The algorithm proposed reduces the problem to an overdetermined linear algebraic system of equations, which may readily be solved to yield the simplified model. When this model approximates adequately the original system, it has many important advantage...

A simple proof of the Cayley-Hamilton theorem for the case of two-dimensional systems is presented. The proof is based on the recursive two-dimensional Leverrier-Faddeeva algorithm.

A new algorithm, adaptive neural net vector quantization (ANNVQ), has been devised for image sequence coding. It is an adaptive extension of a neural network vector quantizer, utilizing a modified form of the self- organizing feature maps learning algorithm. Simulation experiments have been carried out with 4×4 blocks of pixels from a videoconferen...

The two-dimensional modified Cauer form continued fraction expansion has been extended to three-dimensions (3-D), and a circuit implementation is presented. Also, the problem of the state-space realization of 3-D systems that can be expanded into a 3-D modified Cauer form has been considered, resulting in a minimal state-space model realization.

A simple technique is presented for the minimal state space realisation of product factorable two dimensional systems. The application of this method yields the matrices A, b, c<sup>T</sup> and the scalar d of the two dimensional Givone-Roesser state space model, having minimal dimension.

A method for the transfer function computation of a generalized (singular) two-dimensional (2-D) state space model has been presented. The method is based on the Leverrier-Faddeeva algorithm for regular systems. The simplicity of the method is illustrated by an example.

A state-space stability test is proposed that reduces
the stability criteria for two-dimensional (2-D) systems to stability
criteria for 1-D systems. A simple procedure that facilitates the
application of these 1-D stability criteria is presented

Artificial neural system (ANS) classification has been applied to
the total set of states of a finite-state machine operating as part of
an image-sequence coder. It has been found that the classification of
states allows the use of a much smaller number of representation states,
thereby drastically reducing the storage requirements of the
finite-st...

A new two-dimensional (2-D) continued fraction expansion, based on the modified Cauer form, has been formulated. Moreover, a minimal state space model realisation has been derived, based on its signal flow graph, using the proposed 2-D continued fraction expansion.

A simple and systematic algorithm, for the computation of the transfer function of singular two dimensional systems, is presented. The method is based on the Faddeeva algorithm and readily can be implemented on a digital computer. A step by step example is given that illustrates the application of this algorithm.

## Projects

Projects (2)

At present Time I am writing a text describing rules concerning the solution of a Sudoku puzzle for a square containing 9 by 9 elements. Many examples are given to clarify the rules not leaving any doubt about their meaning and ambiguity, to understand step by step the hole procedure. We are not pretenting by all means, that we are presenting a general solution to the very popular and exited problem. The explanation of the rules are boosting safely without errors towards the final end. We have applied these methods to the tough case but not to the extreme one case of a sudoku puzzle, containing 17 elements only !