Nickolas J. Theodorou

Two-dimensional digital filters without overflow oscillations and instability due to finite word length

New criteria for the absence of finite word-length effects, such as overflow oscillations and instability, in two-dimensional digital filters are presented. The criteria are formulated using the state-space representations and are based on results concerning the 2D Lyapunov equation. Several examples illustrate the theoretical results. >

Stability tests for 2-D systems using the Schwarz form and the inners determinants

New stability tests for two-dimensional (2-D) (discrete/continuous) systems using the Schwarz form and the concept of inner determinants are presented. The properties of the Schwarz matrix are used for checking the stability of 2-D systems in state-space. Two innerwise matrices that have inner determinants equivalent to the principal minors of the Hermitian Schur-Cohn/Hermite matrix are introduced. The implementation of these new stability tests for discrete/continuous 2-D systems is discussed. The proposed methods offer a simplification by not requiring the positivity of many polynomials. The theoretical results are illustrated by nontrivial examples. >

Theoretical transmission-line study of symmetrical indoor triple-pole cables for single-phase HF signalling

Theoretical study of symmetrical single-phase indoor tricels is performed with respect to high-frequency (HF) transmission-line modeling, aimed at potential communication applications over the low-voltage (LV) in-house grid. The analysis is based on the fundamental transverse-electro-magnetic (TEM) wave propagation concept, commencing from the three-conductor transmission-line model. In the three-wire cable, any transmission circuit consisting of two conductors-out of all three-is by virtue of symmetry reduced to a two-conductor formulation. The distributed parameters of the resulting model are moreover extracted via proper observation of cables field structure, where complete conformance with the uniform isolated two-conductor line is obtained. Propagation of high frequency signalling transmitted between phase and neutral may thence in practice be treated and formulated independently, as if no ground wire existed. In addition, verification of the TEM mode assumption is demonstrated, and hints on the applicability of the work presented are suggested.

Computation of the stability margin of two-dimensional discrete systems

Two methods of computing the stability margin of two-dimensional discrete systems are presented. The first method uses the Schur-Cohn stability criterion, and the second method is based on results concerning the 1-D Lyapunov equation with complex coefficients. Several examples illustrate the applicability of the two methods. >

A new stability test for two-dimensional discrete systems using bilinear continuous fractions

An algorithm for testing the stability of single-input single-output (SISO) two-dimensional discrete-time systems is presented, using a method in the z-domain exclusively. It is based on expanding the bilinear discrete reactance function into z-domain continuous fractions in a mixed fashion. It is faster than B.M. Karan and M.C. Srivastavas algorithm (1986) and compares favorably with the commonly used tabular form of testing stability of 2-D systems. Two examples are given to illustrate the method and its practical implementation. >

Travelling - Wave Modelling of Uniform Multi - Conductor Transmission Line Networks - Part II : Experimental Validation - Applicability

In Part I of this work, travelling-wave modelling of uniform multi-conductor transmission line networks was analytically established with direct applicability to narrowband transmission, covering any network formed of lossy (in the general case), diagonalisable uniform multi-conductor transmission lines of either distinct or degenerate eigenvalues. As the whole work applies especially in the fleld of Power-Line Communications, in Part II, a validating experimental paradigm is flrst provided using a common cable type for indoor power electric networks. Then, direct applicability to narrowband transmission is addressed, along with potential expandability towards wideband signalling. A comparative evaluation with other existing methods of time-domain modelling is also included and relevant directions for future research are suggested.

Stability of multidimensional systems: overview and new results

Most of the stability results of 2-D discrete systems using the Lyapunov method and the state-space approach are reviewed. The stability of m-dimensional systems is studied through classification of various regions of analyticity, and several theorems and algebraic tests for checking these regions are reviewed. A stability test is presented for two-dimensional systems using the bilinear continued fraction expansion. Numerical examples are presented which support the results. The present study is pertinent to the analysis of the stability of two-dimensional filters, used extensively in image processing.<<ETX>>

On the solution of m-D difference equations via Z-transform and state space analysis

This paper is concerned with the problem of solving m-D difference equations. First, the solution is derived in closed form using the scalar difference equation representation. Then the state-space representation is considered and the transfer function is computed from it using the generalized m-D Leverrier algorithm. The response (solution) is then computed using the inverse m-D Z transform. The theory is illustrated by three examples, one of which was tested on the computer.