Analog and digital filter design is of great importance throughout engineering, applied mathematics, and computer science. Filters are the staple for designers in the controls, signal processing, and communications fields. They are commonly used in a wide variety of systems, such as chemical processing plants, instrumentation, suspension system, modems, and digital cellular phones.
When a designer uses conventional techniques and software to design a filter, the designer receives only one possible filter that meets a set of specifications, yet an infinite number of designs may exist. This book develops alternative techniques and software to return a comprehensive set of designs that meet the specification and represent the infinite design space. Included in the set of designs are filters that have minimal order, minimal quality factors, minimal complexity, minimal sensitivity to pole-zero locations, minimal deviation from a specified group delay, approximate linear phase, and minimized peak overshoot. For digital filters, the design space also includes filters with power-of-two coefficients. These alternative filter designs are crucial when evaluating filters for synthesis in analog circuits, digital hardware, or software.
This book overcomes the gap between filter theory and practice. This books presents new algorithms and designs developed over the last five years. The book includes ready-to-use filter design algorithms and implementations of the algorithms in both MATLAB and Mathematica. In order to make the book accessible to both the practitioner and the researcher, we have divided the book into two parts. Part I reviews conventional filter design techniques, presents several new ready-to-use algorithms, and discusses many case studies. The case studies present filters that cannot be designed with conventional techniques but can be designed with advanced methods. Part II discusses the theory underlying the new advanced design methods. The book also contains appendices to show examples of using advanced filter design software in MATLAB and Mathematica, and give filter design problems for the reader to solve.
In designing analog and digital IIR filters, one generally relies on canned software routines or mechanical procedures that rely on extensive tables. The primary reason for this "black box" approach is that the approximation theory that underlies filter design includes complex mathematics. Unfortunately, the conventional approach returns only one design, and hides a wealth of alternative filter designs that are more robust when implemented in analog circuits, digital hardware, and software.
In this book, we provide advanced techniques to return multiple designs that meet the user specification. The key observations underlying our advanced filter design are that
The theory underlying our advanced techniques is rooted in Jacobi elliptic functions which we use to approximate the magnitude frequency response of the filter. Jacobi elliptic functions are very complex transcendental functions. For many filter orders, however, we derive closed-form solutions to design elliptic filters that only use polynomials, square roots, and logarithms. This breakthrough allows us to derive precise relationships between the user specification, implementation constraints, and the pole-zero locations of the filter. Thus, we have transformed the design space for IIR filters from elliptic function approximation theory into polynomial theory, which can be understood by designers with a knowledge of algebra. In addition, final expressions are simple. Most of elliptic filters can be accurately designed ten to hundred times faster than using classical approach.
The elliptic approximation is the most frequently used function in the design of IIR filters. In the latter part of this book, we explore many of the properties of elliptic functions such as its nesting property. These properties enable us to automate the design of filters using symbolic algebra. Transfer function poles and zeros are obtained by means of simple formulas, thereby freeing the designer from having to rely on extensive tables or canned computer programs. Symbolic design makes it possible to eliminate redundant variables, decrease the filter order, and simplify and approximate the underlying complex relations prior to the final numeric calculations.
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.
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 80 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 Department of Electrical Engineering at the University of Belgrade. He teaches classes in circuit theory, microwave engineering, and digital image processing.
Brian L. Evans is an Assistant Professor in the Department of Electrical and Computer Engineering at The University of Texas at Austin, and the Associate Director of the Laboratory for Vision Systems within the Center for Vision and Image Sciences. His research interests include real-time software, embedded systems, heterogeneous systems, image and video processing systems, system-level design, symbolic computation, and computer-aided design. He has developed numerous computer-aided design tools to prototype and test research ideas, such as the Signals and Systems Pack for Mathematica. His B.S.E.E.C.S. (1987) degree is from the Rose-Hulman Institute of Technology, and his M.S.E.E. (1988) and Ph.D.E.E. (1993) degrees are from the Georgia Institute of Technology. From 1993 to 1996, he was a post-doctoral researcher at the University of California at Berkeley with the Ptolemy Project on system-level design. He is the recipient of a 1997 National Science Foundation CAREER Award. He teaches courses in signal processing and embedded systems.