P. Agathoklis

Adaptive IIR filtering algorithms for system identification: a general framework

Adaptive IIR (infinite impulse response) filters are particularly beneficial in modeling real systems because they require lower computational complexity and can model sharp resonances more efficiently as compared to the FIR (finite impulse response) counterparts. Unfortunately, a number of drawbacks are associated with adaptive IIR filtering algorithms that have prevented their widespread use, such as: convergence to biased or local minimum solutions; requirement of stability monitoring; and slow convergence. Most of the recent research effort on this field is aimed at overcoming some of the above mentioned drawbacks. In this paper, a number of known adaptive IIR filtering algorithms are presented using a unifying framework that is useful to interrelate the algorithms and to derive their properties. Special attention is given to issues such as the motivation to derive each algorithm and the properties of the solution after convergence. Several computer simulations are included in order to verify the predicted performance of the algorithms. >

A new DOA estimation technique based on subarray beamforming

A new direction-of-arrival (DOA) estimation technique using subarray beamforming is proposed. Two virtual subarrays are used to form a signal whose phase relative to the reference signal is a function of the DOA. The DOA is then estimated based on the computation of the phase shift between the reference signal and its phase-shifted version. Since the phase-shifted reference signal is obtained after interference rejection through beamforming, the effect of cochannel interference on the estimation is significantly reduced. The proposed technique is computationally simple, and the number of signal sources detectable is not bounded by the number of antenna elements used. Performance analysis and extensive simulations show that the proposed technique offers significantly improved estimation resolution, capacity, and accuracy relative to existing techniques

The margin of stability of 2-D linear discrete systems

In this paper the margin of stability for a 2-D discrete system is considered. The definition of the margin of stability for the 1-D case is extended to the 2-D case in terms of analytic regions of rational functions in two variables. The relationship between the newly defined stability margin and the impulse response is established. A method to compute the stability margin is presented and illustrated with some examples.

Lower bounds for the stability margin of discrete two-dimensional systems based on the two-dimensional Lyapunov equation

Lower bounds for the stability margin of a 2-D discrete system described with a state-space model are developed. These bounds are given as a function of the positive definite solutions of the 2-D Lyapunov equation. The method presented can be easily extended to the n-dimensional case. >

DEDIP: a user-friendly environment for digital image processing algorithm development

The DEDIP (developmental environment for digital image processing) system is a simple environment for the development of digital image processing applications. It consists of two user interface levels. The low level is compiled software library of digital image processing and system management functions. The high level is a command line interpreter with a set of digital image processing and file management tools. A graphical user interface (GUI) has been developed to increase the user-friendliness of DEDIP at the high level. The GUI is based on the DEDIP functions and the X-window systems. The user has access to all levels and can develop, test, and implement in software digital image processing applications easily. Structured software design techniques of modularity and data encapsulation have been applied in the development of DEDIP.<<ETX>>

Identification and model reduction from impulse response data

Two new algorithms for identification and model reduction of stable linear continuous systems are proposed, based on the weighted impulse response gramians (Agathoklis and Sreeram 1988 b). In identification, the model parameters are obtained from the solution of a linear system of equations with coefficients obtained from the numerical evaluation of the weighted impulse response gramians. The reduction technique is based on retaining part of the original weighted impulse response gramians obtained as the solutions to the Lyapunov equation for the original system in controllability canonical form. This yields different stable models for different values of the weighting factor. The model corresponding to zero weighting factor matches the impulse response norm of the original system and its derivatives exactly. Finally, the method is illustrated by a numerical example and is compared with well-known balanced realization techniques.

Evaluation of quantization error in two-dimensional digital filters

In the evaluation of the quantization error in two-dimensional (2-D) digital filters, a procedure for computing \sum\min{m=0}\max{\infin} \sum\min{n=0}\max{\infin} y^{2}(m,n)= \frac{1}{(2\pij)^{2}}\oint\oint Y(z_{1},z_{2})Y(z_{1}^{-1},z_{2}^{-1}) \frac{dz_{1}dz_{2}}{z_{1}z_{2}} T^{2} = {(z_{1},z_{2}): |z_{1}|=1, |z_{2}|=1} is required. In this paper a condition for a finite quantization error is given and a discussion on the evaluation of the integral based on the residue method is presented. Examples for such an evaluation are given. Furthermore, the salient differences between the one-dimensional (1-D) complex integral evaluation and the two-dimensional one are discussed. Notation: We note with \bar{U}^{2} = {(z_{1}, z_{2}): |z_{1}| \leq 1, |z_{2}| \leq 1 } the closed unit bidisk, with u^{2} = {(z_{1}, z_{2}): |z_{1}| the open unit bidisk, and with T_{2} = {(z_{1}, z_{2}): |z_{1}| = 1, |z_{2}| = 1} the distinguished boundary of the unit bidisk. The 2-D z -transform is defined as Y(z_{1}, z_{2} = \sum\min{m=0}\max{\infin}\sum\min{n=0}\max{\infin} y (m,n)z_{1}^{m}z_{2}^{n} .

Stability and the Lyapunov equation for n-dimensional digital systems

The discrete-time bounded-real lemma for nonminimal discrete systems is presented. Based on this lemma, rigorous necessary and sufficient conditions for the existence of positive definite solutions to the Lyapunov equation for n-dimensional (n-D) digital systems are proposed. These new conditions can be applied to n-D digital systems with n-D characteristic polynomials involving factor polynomials of any dimension, 1-D to n-D. Further, the results in this paper show that the positive definite solutions to the n-D Lyapunov equation of an n-D system with characteristic polynomial involving 1-D factors can be obtained from the solutions of a k-D (0/spl les/k/spl les/n) subsystem and m (1/spl les/m/spl les/n) 1-D subsystems. This could significantly simplify the complexity of solving the n-D Lyapunov equation for such cases.

On the computation of the Gram matrix in time domain and its application

The Gram matrix of the system involves evaluation of the scalar product of repeated integrals and has formerly been computed in frequency domain. A time domain method for evaluation of the Gram matrix is presented. It is based on new properties of the Gram matrix, derived here. A model reduction algorithm based on these properties is presented. The method is illustrated by a numerical example. >

The Lyapunov equation for n-dimensional discrete systems

The necessary and sufficient conditions for the existence of positive definite solutions to the n-D Lyapunov equation are presented. It is shown that there exist n-D stable systems for which no positive definite solutions to the n-D Lyapunov equation exist. Furthermore, it is pointed out that some results on the 2-D Lyapunov equation cannot be extended to either the three- or higher-dimensional case. >