In general about the book

This book develops alternative techniques and software to produce a comprehensive set of designs that meet the specification and represent the infinite design space. This work overcomes the gap between filter theory and practice, and it presents new algorithms and designs developed over the last five years. In this book, the authors provide advanced techniques to return multiple designs that meet the user specification.

The primary benefit of this book is convenient access to the latest advances in algorithms and software for analog and digital IIR filter design. These advanced techniques can design many types of filters that conventional techniques cannot design. A secondary benefit is a large collection of case studies for filter designs that require advanced techniques. Another benefit is a unique treatment of elliptic function filters.

Selected topics chosen from the book chapters can be used in Electronics, Linear Systems and Electric Circuit Theory courses.

The book is supported by the websites which contain the free downloadable filter design software, Mathematica notebooks and MATLAB scripts:

http://galeb.bg.ac.yu/~lutovac
http://iritel.iritel.bg.ac.yu/users/lutovac/www
http://www.rcub.bg.ac.yu/~tosicde

There is also a companion website that accompanies this text:

http://www.prenhall.com/lutovac

Chapter content

The book is divided into 13 chapters.

Chapter 1 presents an overview of basic classes of continuous-time and discrete-time signals. Mathematical representations of signals is discussed, and the two computer environments, MATLAB and Mathematica, which are used to analyze and process signals, are introduced.

The basic definitions and background mathematics that is used in this book is presented in Chapter 2.

In Chapter 3, the authors review the definition and the salient properties of the most important transforms required by the filter design studied in this book. They focus on the phasor transformation, Fourier series and harmonic analysis, Fourier transformation, Laplace transformation, discrete Fourier transform, and Z-transform.

Chapter 4 is intended to review the basics of classic analog filter design. Classification, salient properties and sensitivity of transfer functions are given. The most important analog filter realizations are presented. Detailed case study is given for realization of various transfer functions.

Chapter 5 reviews basic definitions of analog filter design. It introduces straightforward procedures to map the filter specification into a design space. The authors search this design space for the optimum solution according to given criteria. They conclude this chapter by an application example in which they design a robust selective analog filter based on commercially available integrated circuits.

The case studies of optimal analog filters that cannot be designed with classic techniques, and the formal, mathematical framework that underlies their solutions are presented in Chapter 6.

Chapter 7 presents an extensible framework for designing analog filters that exhibit several desired behavioral properties after being realized in circuits. In the framework, authors model the constrained non-linear optimization problem as a sequential quadratic programming problem. They derive the differentiable constraints and a weighted differentiable objective function for simultaneously optimizing the behavioral properties of magnitude response, phase response, and peak overshoot and the implementation property of quality factors.

Chapter 8 is intended to review the basics of classic digital IIR filter design. Classification, salient properties and sensitivity of transfer functions in the z-domain are given. The most important digital filter realizations are presented. For each realization complete design equations and procedures that make the design easily applicable to a broad variety of digital filter design problems are provided.

Chapter 9 reviews basic definitions of digital IIR filter design. It introduces straightforward procedures to map the filter specification into a design space. The authors search this design space for the optimum solution according to given criteria. They conclude this chapter by several important application examples in which they design low-sensitivity selective multiplierless IIR filters, power-of-two IIR filters, half-band IIR filters, 1/3-band filters, narrow-band IIR filters, Hilbert transformers, and zero-phase IIR filters. Each example design is followed by a comprehensive step-by-step procedure for computing the filter coefficients.

In Chapter 10, they present case studies of optimal digital filters that cannot be designed with classic techniques, and the formal, mathematical framework that underlies their solutions.

Chapter 11 presents an extensible framework for the simultaneous constrained optimization of multiple properties of digital IIR filters. The framework optimizes the pole-zero locations for behavioral properties of magnitude and phase response, and the implementation property of quality factors, subject to constraints on the same properties. The authors formulate the constrained nonlinear optimization problem as a sequential quadratic programming problem.

Chapter 12 introduces the basic Jacobi elliptic functions and reviews the most important relations between them. Several related theorems not found in standard textbooks are presented. Various useful approximation formulas are offered to facilitate the derivation of elliptic rational functions. A nesting property of the Jacobi elliptic functions is derived. In this chapter the authors present a novel approach to the design of elliptic filters in which they use exact closed-form expressions based on the nesting property.

In Chapter 13, authors introduce the elliptic rational function as a natural generalization of the Chebyshev polynomial and they bypass mathematical theory of special functions required in the previous chapter. They prefer to give a reader an intuitive feel of the basic properties of the elliptic rational function. Their goal is to build the knowledge of the elliptic rational function using simple algebraic manipulations, even, without mentioning the Jacobi elliptic functions.

Useful book

This book opens up completely new vistas in basic filter design, regardless of the technology. The authors show that the conventional filter types (e.g. Butterworth, Chebyshev, Elliptic) are not unique solutions to a given set of specifications; much rather they are special cases of a continuum of solutions, all of which, while satisfying the specifications, permit tradeoffs to be made between a variety of optimizations that were considered inaccessible and unachievable in the past.

Since the essence of the book is to loosen the rigidity, in terms of options and optimization, that the previous "preliminary design ritual" demanded, it can be used as a new versatile preliminary design routine for any kind of subsequent filter realization, be it e.g., LC, active RC, digital or switched-capacitor. Indeed, the authors demonstrate their new and versatile design technique in conjunction with all of these filter types, and many more.

About the authors

Miroslav D. Lutovac is a chief scientist at the Institute for Research and Development in Telecommunications and Electronics (IRITEL) and is an Associate Professor in the School of Electrical and Computer Engineering, which is located at the University of Belgrade in Belgrade, Yugoslavia. His research interests include theory and implementation of active, passive, and digital networks and systems, filter approximation, symbolic analysis and synthesis of digital filters, and multiplierless digital IIR filter design. He has published over 100 papers in these fields. He received his B.Sc. (1981), M.Sc. (1985), and D.Sc. (1991) degrees in Electrical Engineering from the University of Belgrade in Belgrade, Yugoslavia. He has managed several national projects on multichip module design and voice delta coders. He teaches courses in electronics, computer-aided design, digital signal processing, and filter analysis and design.

Dejan V. Tosic is an Associate Professor in the School of Electrical and Computer Engineering at the University of Belgrade in Belgrade, Yugoslavia. His research interests include circuit theory and analysis, filter design and synthesis, neural networks, microwave circuits, and computer-aided design. He has published over 100 papers in these fields. He is currently concentrating his research efforts on creating a general framework for the symbolic analysis of linear circuits and systems, which is suitable for research, industrial, and educational applications. Using this framework, he is developing design automation tools for optimizing the design and synthesis of analog and digital filters. He received his B.Sc.\ (1980), M.Sc.\ (1986), and D.Sc.\ (1996) degrees in Electrical Engineering from the University of Belgrade in Belgrade, Yugoslavia. In 1992, he won the Teacher of the Year Award from the School of Electrical and Computer Engineering at the University of Belgrade. He teaches classes in circuit theory, microwave engineering, and digital image processing.

Brian L. Evans received his BSEECS degree from the Rose-Hulman Institute of Technology in May 1987 and obtained his MSEE and Ph.D. degrees from the Georgia Institute of Technology in December 1998 and September 1993, respectively. From 1993 to 1996, he enjoyed life in the San Francisco Bay Area as a postdoctoral researcher at the University of California at Berkeley, where he worked with the Ptolemy Project. Ptolemy is a research project and software environment focused on design methodology for signal processing, communications, and controls systems. In addition to Ptolemy, he has played a key role in the development and release of six other computer-aided design frameworks. He is the primary architect of the Signals and Systems Pack for Mathematica, which has been on the market since October 1995. He is currently an Assistant Professor in the Department of Electrical and Computer Engineering at the University of Texas at Austin. He is the Director of the Embedded Signal Processing Laboratory within the Center for Vision and Image Sciences. His research interests include real-time embedded systems; signal, image, and video processing systems; system-level design; symbolic computation; and filter design. At UT Austin, he developed and currently teaches Multidimensional Digital Signal Processing, Embedded Software Systems, and Real-Time Digital Signal Processing Laboratory, in part to respond to the needs of industry but also to recruit students for his research group. He is an Associate Editor of the IEEE Transactions on Image Processing and is the recipient of a 1997 National Science Foundation Career Award.