Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

System Identification I

There has been a great deal of material in the area of discrete-time transforms that has been published in recent years. This book does an excellent job of presenting important aspects of such material in a clear manner. The book has 11 chapters and a very useful appendix. Seven of these chapters are essentially devoted to the Fourier series/transform, discrete Fourier transform, fast Fourier transform (FFT), and applications of the FFT in the area of spectral estimation. Chapters 8 through 10 deal with many other discrete-time transforms and algorithms to compute them. Of these transforms, the KarhunenLoeve, the discrete cosine, and the Walsh-Hadamard transform are perhaps the most well-known. A lucid discussion of number theoretic transforms i5 presented in Chapter 11. This reviewer feels that the authors have done a fine job of compiling the pertinent material and presenting it in a concise and clear manner. There are a number of problems at the end of each chapter, an appreciable number of which are challenging. The authors have included a comprehensive set of references at the end of the book. In brief, this book is a valuable contribution to the general areas of signal processing and communications. It can be used for a graduate level course in perhaps two ways. One would be to cover the first seven chapters in great detail. The other would be to cover the whole book by focussing on different topics in a selective manner. This book  by  Elliott  and Rao  is extremely  useful to researchers/engineers who are working  in the areas of signal processing and communications. It i s also an excellent reference book, and hence a valuable addition to one’s library

http://ieeexplore.ieee.org/iel5/5/31347/01457444.pdf

Multirate digital signal processing

A convergence analysis is performed for a recursive prediction error algorithm based on nonlinear ODEs and the midpoint integration algorithm. Several conditions are formulated such that the stability of an associated differential equation can be tied to the local and global convergence properties of the algorithm. This is used to show that the algorithm converges to a minimum point of the criterion function, which may or may not be unique. A consequence is that convergence to the true parameters is possible. As compared to previous work, complete system assumptions are integrated in the analysis, thereby generalising previous results. The theoretical analysis of this paper is complemented with numerical examples and with live data experiments.

Convergence analysis and experiments using an RPEM based on nonlinear ODEs and midpoint integration

Nonlinear system identification—Application for industrial hydro-static drive-line

In this paper, several advanced data-driven nonlinear identification techniques are compared on a specific problem: a simplified glucoregulatory system modeling example. This problem represents a challenge in the development of an artificial pancreas for T1DM treatment, since for this application good nonlinear models are needed to design accurate closed-loop controllers to regulate the glucose level in the blood. Block-oriented as well as state-space models are used to describe both the dynamics and the nonlinear behavior of the insulin-glucose system, and the advantages and drawbacks of each method are pointed out. The obtained nonlinear models are accurate in simulating the patient's behavior, and some of them are also sufficiently simple to be considered in the implementation of a model-based controller to develop the artificial pancreas.

Comparison of several data-driven nonlinear system identification methods on a simplified glucoregulatory system example

In this paper, a novel method for designing filters generating the discrete-time analytic signal is proposed. The technique relies on the rotation of the pole-zero plot of a low-pass filter. As a consequence, the classical design methods can be reused. This method is compared to a direct filter design approach.

Johan Schoukens

Papers

Convergence analysis and experiments using an RPEM based on nonlinear ODEs and midpoint integration

Nonlinear system identification—Application for industrial hydro-static drive-line

Comparison of several data-driven nonlinear system identification methods on a simplified glucoregulatory system example

Comparison of Filter Design Methods to generate Analytic Signals

Generation of enhanced initial estimates for wiener systems and harnrnerstein systems