UNITED STATES PATENT AND TRADEMARK OFFICE
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`
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
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`Case IPR2022-01059
`U.S. Patent No. 10,779,080
`______________________
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`
`GOOGLE LLC,
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`Petitioner
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`v.
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`JAWBONE INNOVATIONS, LLC,
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`Patent Owner
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`
`
`
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`
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`Declaration of Shauna L. Wiest Regarding Widrow
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`GOOGLE EXHIBIT 1029
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`Declaration of Shauna L. Wiest
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`I, Shauna L. Wiest, state and declare as follows:
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`I.
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`Introduction
`1.
`I have prepared this Declaration in connection with Google
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`LLC’s (“Petitioner”) Petition for Inter Partes Review of U.S. Patent No.
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`10,779,080, which I understand will be filed concurrently with this
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`Declaration.
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`2.
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`I am currently a senior research analyst with the Research &
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`Information Services team at Finnegan, Henderson, Farabow, Garrett &
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`Dunner LLP located at 901 New York Avenue, NW, Washington, DC 20001-
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`4413.
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`3.
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`I am over eighteen years of age, and I am competent to make this
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`Declaration. I make this Declaration based on my own personal knowledge,
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`and my professional knowledge of library science practices.
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`4.
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`I earned a Master of Science in Library Science degree from the
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`University of North Carolina at Chapel Hill in 1999, and a Bachelor of Arts
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`in Political Science degree from the University of California at San Diego in
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`1989. I have worked as a law librarian for over twenty years. I have been
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`employed in the Research & Information Services Department at Finnegan,
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`Henderson, Farabow, Garrett & Dunner LLP since 2021. Before that, from
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`2000-2015, I was employed as a Law Librarian at Stoel Rives LLP, and from
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`Declaration of Shauna L. Wiest
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`2015-2016, I was employed as a Competitive Intelligence Specialist for
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`Nossaman LLP.
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`II.
`
`Standard Library Practice for Receiving, Cataloging, and
`Making Materials Publicly Available
`4.
`I have knowledge of and experience with standard library practices
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`regarding the receipt, processing, cataloging, shelving, and making materials
`
`available to the public. I am fully familiar with and have knowledge of and
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`experience with the Machine-Readable Cataloging (MARC) system, an
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`industry-wide standard that libraries use to catalog materials.
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`5.
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`The MARC system was developed during the 1960s to standardize
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`bibliographic records so they could be read by computers and shared among
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`libraries. By the mid-1970s, MARC had become the international standard for the
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`storage of bibliographic data and cataloguing. It is still used today. Many libraries
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`provide public access to their MARC records via the Internet and/or their electronic
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`cataloging systems at the library.
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`6.
`
`Based on standard library practice, when a library receives an item,
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`it stamps (or labels) the item with the library name and often with a date that is
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`within a few days or weeks of receipt. Next, the library will catalog the item
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`within a matter of a few days or weeks of receiving it.
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`7.
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`Generally, after an item is cataloged, the public may access the item
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`by searching a catalog, browsing the library shelves, and either requesting or
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`Declaration of Shauna L. Wiest
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`electronically accessing the item from the library. Standard library practice is to
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`make the item available to the public within a few days or weeks of cataloging it.
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`III. Print Public Holdings for Widrow
`8.
`This Declaration relates to the dates of receipt and public
`
`availability of the following: Bernard Widrow and Samuel D. Stearns,
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`Adaptive Signal Processing, Chapters 1, 2, and 6, Prentice-Hall, Inc. (1985)
`
`(ISBN 0130040290) (Widrow). Exhibit 1020 to the concurrently filed Petition
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`is a true and accurate copy of Widrow held by the Linda Hall Library in Kansas
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`City, Missouri.
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`9.
`
`As detailed below, I have reviewed the print public holdings
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`information from the Linda Hall Library in Kansas City, Missouri for its
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`copy of Widrow.
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`10. Appendix A to this declaration is a true and accurate copy of the
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`front matter, title pages, table of contents, and chapters one, two, and six of the
`
`Widrow text held by the Linda Hall Library. The date stamp on the front matter
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`indicates that Widrow was received by the Engineering Societies Library on June
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`24, 1985.
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`11. Appendix B to this declaration is a true and accurate copy of the
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`public catalog record from the Linda Hall Library for its copy of Widrow,
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`including holdings and location information, which was downloaded from
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`Declaration of Shauna L. Wiest
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`https://catalog.lindahall.org/permalink/01LINDAHALL_INST/19lda7s/alma992
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`403023405961 on May 12, 2022.
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`12. Appendix B sets forth the holdings and onsite location information
`
`for members of the interested public seeking to locate Widrow. The public
`
`catalog record indicates that Widrow is available in the Linda Hall Library Books
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`on the 2nd Floor at Call Number TK5102.5 .W537 1985 ESL. The public catalog
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`record also contains a “local note” indicating that Widrow was transferred from
`
`the Engineering Societies Library to the Linda Hall Library in January 1995.
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`13. Based on the evidence presented above, it is my professional
`
`opinion that Exhibit 1020 is an authentic document, which would have been
`
`made publicly available and publicly accessible at the Engineering Societies
`
`Library from a few days or weeks after June 24, 1985, through January 1995, and
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`then at the Linda Hall Library at “Linda Hall Library Books - 2nd Floor” upon its
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`transfer in January 1995.
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`IV. Conclusion
`14.
`In signing this Declaration, I understand it will be filed as
`
`evidence in a contested case before the Patent Trial and Appeal Board of the
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`United States Patent and Trademark Office. I understand I may be subject to
`
`cross-examination in this case and that cross-examination will take place
`
`within the United States. If cross-examination is required of me, I will appear
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`Declaration of Shauna L. Wiest
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`for cross-examination within the United States during the time allotted for
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`cross-examination.
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`15.
`
`I declare that all statements made herein of my knowledge are
`
`true, that all statements made on information and belief are believed to be
`
`true, and that these statements were made with the knowledge that willful
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`false statements and the like so made are punishable by fine or imprisonment,
`
`or both, under Section 1001 of Title 18 of the United States Code.
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`Executed on May 25, 2022.
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`
`
`
`
`Shauna L. Wiest
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`Page 6 of 6
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`Appendix A
`Appendix A
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`Viy.Vais
`Rar
`PROCESSING
`Bernard Widrow
`
`Samuel D. Stearns
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`Page 8 of 70
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`

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`ADAPTIVE
`SIGNAL
`PROCESSING
`
`Bernard Widrow ©
`
`Stanford University
`
`Samuel D. Stearns
`Sandia National Laboratories
`
`¢
`
`Prentice-Hall, Inc.
`Englewood Cliffs, N.J. 07632
`
`Page 9 of 70
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`

`

`PRENTICE-HALL SIGNAL PROCESSING SERIES
`
`Alan V. Oppenheim, Editor
`
`ANDREWSAND Hunt Digital Image Restoration
`BRIGHAM’
`The Fast Fourier Transform
`BuRDIC
`Underwater Acoustic System Analysis
`CASTLEMAN_Digital Image Processing
`COWAN AND GRANT Adaptive Filters
`CROCHIERE AND RABINER Miultirate Digital Signal Processing
`DUDGEON AND MERSEREAU Miulti-Dimensional Digital Signal Processing
`HAMMING_Digital Filters, 2e
`HAYKIN, ET AL. Array Signal Processing
`JAYANT AND NOLL Digital Coding of Waveforms
`LEA, ED.
`Trends in Speech Recognition
`Lim=Speech Enhancement
`MCCLELLAN AND RADER
`Number Theory in Digital Signal Processing
`OPPENHEIM, ED.
`Applications of Digital Signal Processing
`OPPENHEIM AND SCHAFER
`Digital Signal Processing
`OPPENHEIM, WILLSKY, WITH YOUNG_Signals and Systems
`RABINER AND GOLD
`Theory and Application of Digital Signal Processing
`RABINER AND SCHAFER_Digital Processing of Speech Signals
`ROBINSON AND TREITEL
`Geophysical Signal Analysis
`TRIBOLET
`Seismic Applications of Homomorphic Signal Processing
`WIDROW AND STEARNS'~ Adaptive Signal Processing
`
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`Library of Congress Cataloging in Publication Data
`
`Widrow,Bernard, (date)
`Adaptive signal processing.
`
`(Prentice-Hall signal processingseries)
`Includes index.
`1. Adaptive signal processing.
`Samuel D.
`II. Title.
`III. Series.
`TK5102.5.W537
`1985
`621.38'043
`ISBN 0-13-004029-0
`
`I. Stearns,
`
`84-18057
`
`Editorial/production supervision and
`interior design: Tracey L. Orbine
`Cover design: Sue Behnke
`Manufacturing buyer: Anthony Caruso
`
`ENGINEERING SOCIETIES LIBRARY
`
`y
`
`JUN 24 1985
`
`REVIEW
`
`© 1985 by Prentice-Hall, Inc., EnglewoodCliffs, New Jersey 07632
`
`All rights reserved. No part of this book may be
`reproduced,in any form or by any means,
`without permission in writing from the publisher.
`Printed in the United States of America
`0987654321
`
`b a ‘ 2e
`2%se
`
`ISBN O-13-004029
`
`O01
`
`Prentice-Hall International, Inc., London
`Prentice-Hall of Australia Pty. Limited, Sydney
`Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro
`Prentice-Hall Canada Inc., Toronto
`Prentice-Hall Hispanoamericana, S. A., Mexico
`Prentice-Hall of India Private Limited, New Delhi
`Prentice-Hall of Japan, Inc., Tokyo
`Prentice-Hall of Southeast Asia Pte. Ltd., Singapore
`Whitehall Books Limited, Wellington, New Zealand
`
`Page 11 of 70
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`BQ. 3 £07
`
`This book is dedicated, to the memory of Moses Widrow, William
`K. Linvill, and Thomas J. Flanagan. It is also dedicated to the
`cause of peace on earth. We hopeandtrust that its contents will be
`used to improve the lot of mankind everywhere.
`
`GYIOS
`RxSubBOS:
`
`LINDA HALL LIBRARY
`Kansas City, Mo.
`
`Page 12 of 70
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`part|
`
`GENERAL INTRODUCTION
`
`(Chapters 1 and 2)
`
`OBJECTIVES OF PART|
`
`In the first two chapters of this book we have three major objectives. Thefirst
`is to introduce the basic meaning of “adaptation” (or “adaption’’) in the
`engineering sense, and to set adaptive signal processing into the general
`signal processing context.
`The second objective is to describe the adaptive linear combiner, which
`is the simplest and most widely applicable adaptive processor.It is the basic
`adaptive device that will be used exclusively through Chapter 6, as well as in
`muchof the rest of the text.
`The third objective is to persuade the reader to think of the overall
`processof adaptation in geometrical terms. Wewish to think of adaptation as
`a procedure for moving generally downhill on a ‘‘performance surface’”’ like
`the one shown on page 2, which is the L-dimensional surface in (L +
`1)-dimensional space formed by plotting the mean-square error versus the
`fur.adaptive parameters. These geometrical concepts and terms are described in
`Chapter2.
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`Performance surface
`
`
`
`M€an-squareerror
`
`
`anvalues
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`—_--_—
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`2
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`chapter 1
`
`Adaptive Systems
`
`DEFINITION AND CHARACTERISTICS
`
`adapt, v.t., 1. to make suitable to requirements or conditions; adjust or modifyfittingly;
`. v.i., 2. to adjust oneself to different conditions, environments, etc. (Random House
`Dictionary, 1971)
`
`In recent years, a growing field of research in “adaptive systems” has resulted
`in a variety of adaptive automatons whose characteristics in limited ways resemble
`certain characteristics of living systems and biological adaptive processes. According
`to the Random House Dictionary, some of the meanings of “adaptation”are:
`
`the state of being adapted; adjustment. 3. Biol. a. any
`the act of adapting. 2.
`1.
`alteration in the structure or function of an organism or anyofits parts that results
`from natural selection and by which the organism becomesbetterfitted to survive and
`multiply in its environment. b. a form orstructure modified to fit changed environ-
`ment. 5. Physiol.
`the decrease in response of sensory receptor organs, as those of
`vision, touch, temperature, olfaction, audition, and pain, to changed, constantly ap-
`plied, environmental conditions. 6. Ophthalm.
`the regulating by the pupil of the
`quantity oflight entering the eye. 7. Sociol. a slow, usually unconscious modification of
`individual andsocial activity in adjustment to cultural surroundings.
`
`It will be noted that the definition above is expressed primarily in terms of
`biological adaptation to environment. The same definitions serve at least to some
`extent for “artificial” or human-made adaptive systems, which are the central
`concern of this book.
`An adaptive automatonis a system whosestructureis alterable or adjustable in
`such a way that its behavior or performance (according to some desired criterion)
`improves through contact with its environment. A simple example of an automaton
`or automatic adaptive system is the automatic gain control (AGC) used in radio and
`television receivers. The function of this circuit is to adjust the sensitivity of the
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`3
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`following characteristics:
`
`1. They can automatically adapt (self-optimize) in the face of changing (nonsta-
`tionary) environments and changing system requirements.
`2. They can betrained to perform specific filtering and decision-makingtasks.
`Synthesis of systems having these capabilities can be accomplished automati-
`cally through training. In a sense, adaptive systems can be “programmed” by
`a training process.
`dase elt Les deege ptt 7?
`3. Because of the above, adaptive systems do not require the elaborate synthesis
`procedures usually needed for nonadaptive systems. Instead, they tend to be
`“self-designing.”
`4. They can extrapolate a model of behavior to deal with newsituations after
`having been trained ona finite and often small number of training signals or
`patterns.
`5. To a limited extent, they can repair themselves; that is, they can adapt around
`certain kinds of internal defects.
`6. They can usually be described as nonlinear systems with time-varying parame-
`ters.
`they are more complex and difficult to analyze than nonadaptive
`tes 7, Usually,
`systems, but they offer the possibility of substantially increased system perfor-
`mance when inputsignal characteristics are unknown or time varying.
`
`+,+«
`
`AREAS OF APPLICATION
`
`Recentprogress in microcircuit design and production hasresulted in very compact,
`economical, and reliable signal processors thatrival biological nervous systems in
`size andare clearly superior to biological systemsin speed. The gesult has been a
`very fast-growing field of applications for all
`types of digital signal processing,
`including adaptive processing. Current applications for adaptive systems are in such
`fields as communications, radar, sonar, seismology, mechanical design, navigation
`systems, and biomedical electronics.
`Part IV of this book concernscertain classes of applications, and the chapter
`headings provide a rough picture of the application areas. Chapter 9 covers adaptive
`modeling and system identification, in which an adaptive system models an un-
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`that is, control systems whose
`Chapter 11 is on adaptive control systems,
`characteristics change with time and adapt to the environment. An example is the
`flight control system whose gain and response times change with air density.
`Adaptive noise canceling, discussed in Chapter 12, has been applied to areas such as
`speech communications, electrocardiography, and seismic signal processing. Adap-
`tive noise canceling is in fact applicable to a wide variety of signal-enhancement
`situations, because noise characteristics are not often stationary in real-world
`situations. Chapters 13 and 14, on adaptive arrays, describe an area where adaptive
`signal processing concepts have proved to beespecially useful.
`
`GENERAL PROPERTIES
`
`The essential and principal property of the adaptive system is its time-varying,
`self-adjusting performance. The need for such performance mayreadily be seen by
`realizing that if a designer develops a system of fixed design which he or she
`considers optimal, the implications are that the designer has foreseen all possible
`input conditions, at least statistically, and knows what he or she would like the
`system to do undereach of these conditions. The designer has then chosena specific
`criterion whereby performanceis to be judged, such as the amountoferror between
`the output of the actual system and that of some selected model or “ideal” system.
`Finally,
`the designer has chosen the system that appears best according to the
`performancecriterion selected, generally choosing this system from anapriori
`restricted class of designs (such as linear systems).
`In many instances, however, the complete range of input conditions may not
`be known exactly, or even statistically; or the conditions may change from time to
`time. In such circumstances, an adaptive system that continually seeks the optimum
`within an allowed class of possibilities, using an orderly search process, would give
`superior performance compared with a system of fixed design.
`By their very nature, adaptive systems must be time varying and nonlinear.
`Their characteristics depend, among other things, on their inputsignals. If an input
`signal x, is applied, an adaptive system will adapt to it and produce an output—let
`us call it y,. If another input signal, x, is applied, the system will adapt to this
`second signal and will again produce an output—let us call it,
`this time, y).
`Renerally the form or the structure or the adjustments of the adaptive system will
`beslifferentforehe two different inputs. If the sum of the two inputs is applied to
`age
`0
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`GeneralIntroduction
`
`Part|
`
`v1 + ¥2
`Yt ya: X2@
`
`x
`
`Figure 1.1 The loweroutput, y,, is equal
`to y + y if H is a linear system. If H
`is adaptive, y, is generally different from
`
`the adaptive system, the latter will adapt to this new input—butit will produce an
`output that will generally not be the same as y, + y,, the sum of the outputs that
`would have corresponded to inputs x, and x,. In such a case,
`asillustrated in
`Figure 1.1,
`the principle of superposition does not work as it does with linear
`systems. If a signal is applied to the input of an adaptive system to test its response
`characteristics, the system adaptsto this specific input and thereby changes its own
`form. Thusthe adaptive system is inherently difficult to characterize in conventional
`terms.
`Within the realm of nonlinear systems, adaptive systems cannot be dis-
`tinguished as belonging to an absolutely clear subset. However,
`they have two
`features that generally distinguish them from other forms of nonlinear systems.
`First,adaptive systems are adjustable, and their adjustments usually depend on
`nite-time average, signal characteristics rather than on instantaneous values of
`signals or instantaneous values of the internal system states. Second, the adjust-
`ments of adaptive systems are changed purposefully in order to optimize specified
`performance measures.
`Certain formsofadaptivesystems.become.linear,systems .when-their-adjyst-
`ments, areheld.constant,afteradaptation..These may becalled ‘elinear_adaptive
`systems.” ‘They are very useful; they tend to be mathematically tractable; and they
`“dré"penerally easier to design than other forms of adaptive systems.
`
`OPEN- AND CLOSED-LOOP ADAPTATION
`
`Several waysto classify adaptive schemes have been proposed in theliterature. It is
`most convenient here to begin by thinking in terms of open-loop and closed-loop
`adaptation. The open-loop adaptive process involves making measurementsof input
`or environmental characteristics, applying this information to a formula or to a
`computational algorithm, and using the results to set the adjustments of the adaptive
`system. Closed-loop adaptation, on the other hand, involves automatic experimen-
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`Chap. 1
`
`Adaptive Systems
`
`7
`
`tation with these adjustments and knowledge of their outcome in order to optimize a
`measured system performance. The latter process may be called adaptation by
`“performance feedback.”
`The principles of open- and closed-loop adaptation are illustrated in Figures
`1.2 and 1.3. In both casesit is helpful to envisage the adaptive processas it might be
`performed manually by a human operator or “supervisor.” In Figures 1.2(a) and
`1.3(a) the supervisor is shown adjusting the controls of the processor by reading a
`display that registers measurementsof the preselected performancecriterion. In the
`epenclopp.system.this.criterion.is.a.chasacteristic.of.thesinput-signalandperhaps,
`_other,datazand in.the-closed-loop.systemitis_also,a-functionofthe.outpulsignals
`‘The adjustments in Figure 1.3 are made even though the operator may have no
`knowledge of what is inside the processor or of the functions performed by the
`controls. The operator does not process the input signal; he or she only controls
`the adjustments of the processor to keep its performance optimized according to the
`preselected criterion. Thus the operator’s function is purely supervisory, and in real
`automatic adaptive systems the operator is replaced by computational or “adaptive”
`algorithms, as suggested by Figures 1.2(b) and 1.3(b). The “other data” in these
`figures may be data about
`the environment of the adaptive system, or in the
`closed-loop case, it may be a desired version of the outputsignal.
`
`Processor
`
`Input
`signal
`
`Other
`data
`
`Output
`
`signal
`
`
`
`
`Signal
`processor
`
`Display
`
`(a)
`
` Input
`
`
`Processor
`
`Adaptation
`algorithm
`
`signal
`
`Other
`data
`
`Output
`signal
`
`(b)
`
`Figure 1.2 Open-loop adaptation:(a) concept; (b) equivalent system.
`
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`GeneralIntroduction
`
`Part |
`
`ae
`
`Processor
`
`signal
`
`Output
`
`Other
`
`calculation
`
`signal
` Input
`| Performance
`data N
`
` Performance
`display
`
`
`Input
`signal
`
`(a)
`
`
`
`
`
`
`Performance
`calculation
`
`Adaptation
`algorithm
`
`Output
`signal
`
`Other
`data
`
`(b}
`
`Figure 1.3. Closed-loop adaptation.
`
`When designing an adaptive process, many factors determine the choice of
`closed-loop versus open-loop adaptation. che availabilityof,input Signalsand |
`-berformance-indicatingSignals.is Amajor.consideration, Also, the amount of ‘com-
`puting capacity and the type of computer required to implement the open-loop and
`closed-loop adaptation algorithms will generally differ. Certain algorithms require
`the use of a general-purpose digital computer, whereas other algorithms could be
`implemented far more economically with special-purpose chips or other apparatus.
`Someof these structural considerations are discussedin later chapters. It is difficult
`to develop general principles to guide all choices, but several advantages and a few
`disadvantages of closed-loop adaptation, which is the main subject of this book, can
`be pointed out here.
`Closed-loop adaptation has the advantage of being workable in many applica-
`tions where no analytic synthesis procedure either exists or is known; for example,
`whereerrorcriteria other than mean-square are used, where systems are nonlinear or
`time variable, where signals are nonstationary, and so on. Closed-loop adaptation
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`Chap. 1
`
`Adaptive Systems
`
`9
`
`can also be used effectively in situations where physical system componentvaluesare
`variable or inaccurately known. Closed-loop adaptation will find the best choice of
`componentvalues. In the eventof partial system failure, an adaptation mechanism
`that continually monitors performance will optimize this performance by adjusting
`and reoptimizing the intact parts. As a result, system reliability can often be
`improved by the use of performance feedback.
`The closed-loop adaptation process is not always free of difficulties, however.
`In certain situations, performance functions do not have unique optima. Automatic
`optimization is an uncertain process in such situations. In other situations,
`the
`closed-loop adaptation process, like a closed-loop control system, could be unstable.
`The adaptation process could diverge rather than converge. In spite of these
`possibilities, performance feedback is a powerful, widely applicable technique for
`implementing adaptation. Most of the adaptive processes described in this book will
`be closed-loop processes utilizing performance feedback.
`
`APPLICATIONS OF CLOSED-LOOP ADAPTATION
`
`Let us now consider briefly some applications of the closed-loop, performance
`feedback concept. These will anticipate the applications chapters in Part IV, begin-
`ning with Chapter 9.
`We begin by representing the performance feedback process [Figure 1.3(b)]
`more specifically in Figure 1.4. We call the input signal x and define a “desired
`fesponse””signal_d,.which is.assumed to.representthe. desiredoutputofthe.adaptive,,
`(system. The Signald‘is,forourpurposehere, the “otherdata’in Figure 1.3(b).
`Theerror signal, ¢, is the difference between the desired output signal and the
`actual output signal, y, of the adaptive system. Using the error signal, an adaptive
`algorithm adjusts the structure of the adaptive system, thus altering its response
`characteristics by minimizing some measureoftheerror, thereby closing the perform-
`ance loop.
`Different structures are possible for the adaptive system, and these are dis-
`cussed later, beginning in Chapter 2. Adaptive algorithms for adjusting these
`structures are also discussed later, beginning in Chapter 4. Here we wish only to
`show in a general way how the schemein Figure 1.4 is applied in practical situations.
`
`d (desired output)
`
`
` y (output)
`é (error)
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`Processor
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`Figure 1.4 Signals in closed-loop
`adaptation.
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`General Introduction
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`Figure 1.5 Examples showing how the
`configuration in Figure 1.4 may be
`applied: (a) prediction; (b) system
`identification (modeling); (c) equalization
`(deconvolution,inversefiltering, inverse
`modeling); (d) interference canceling.
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`Chap.1
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`Adaptive Systems
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`11
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`Some examplesof applications are given in Figure 1.5. Notice that Figure 1.4,
`which illustrates the basic closed-loop adaptive process, is simplified slightly and
`embeddedin each part of this figure, and that the application determines how the
`desired signal, d, is obtained.
`The prediction application in Figure 1.5(a) is perhaps the simplestof the four.
`The desired signal is the input signal, s, and a delayed version of the latter is sent to
`the adaptive processor, which must therefore try to ¢predict’-the-gureentanput
`Signal.in,order,tohaye_y,cancel.d_.anddrive.s-toward.zerg,Predictionis .used.in,
`signalencodingandnoise,reduction,and is discussed in Chapters8,9, and 12.
`The system identification application in Figure 1.5(b) is also easy to under-
`stand. Here a broadbandsignal, s, is the input to the adaptive processor as well as
`to an unknown “plant” (a term originating in the control literature). To reducee,
`the adaptive processor tries to emulate the plant’s transfer characteristic. After
`adaptation the plant is “identified” in the sense that its transfer function can be
`specified as essentially the same as that of the adaptive processor. Adaptive system
`identification or modeling can be used as such, to model a slowly varying plant
`whose input and output signals are available, for example, in vibration studies of
`mechanical systems. It can also be used in many other ways, some of which are
`described in Chapters 9 and 11.
`The inverse modeling application [Figure 1.5(c)] is discussed primarily in
`Chapter10, andits uses in control are discussed in Chapter 11. In this application
`theadaptiveprocessor attempts.torecoveradelayedversion.ofthe-signal, s, which
`is assumed to have been altered by the slowly varying plant and to contain additive
`noise. Thedelay in thefigure is to allow for the delay, or propagation time, through
`the plant and the adaptive processor. Adaptive equalization could be used to undo
`(deconvolve) the effects of a transducer, a communication channel, or some other
`system, or to produce an inverse model of an unknownplant. It is also applicable in
`the design of digital filters, as well as in adaptive control problems, and so on.
`Finally, Figure 1.5(d) showsthe adaptive processor in an interference-canceling
`configuration. Herethesignal, s, is corrupted by additive noise, n, and a distorted
`but correlated version of the noise, n’, is also available. The.goal-of-theadaptaye
`~Processor,inthisfase istoproduce.an.output,. athat.closelyresembles.n,sQthat,the
`overalloutput,:¢-will-closely_resemble_s., Wewill show, under certain very broad
`conditions, that the optimal adaptive processor is that which minimizes the mean-
`square value of e. The subject of adaptive interference canceling is discussed in
`Chapters 12 through 14.
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`EXAMPLE OF AN ADAPTIVE SYSTEM
`By now wehave seen that adaptive signal processingis really a very general and
`basic term which implies the.use.of,time-varying_-self-adiusting-sisnal-processors.
`We think of the performance of these’ systems as being purposeful, useful, and
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`12
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`GeneralIntroduction
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`Part|
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`sometimeseven “intelligent” in a limited sense. Before concluding this introductory
`chapter we introduce just one specific example of such a system, to provide a more
`concreteillustration of adaptation in general and closed-loop adaptation in particu-
`lar. We will use the “prediction” application in Figure 1.5(a), keeping in mindthat
`in doing so we have a very restricted and specific example of a very broad and
`general class of systems.
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`Figure 1.7 Signals in the adaptive predictor in Figure 1.6. The error (2) becomes
`nearly zero as the system learns to predict
`the input (x) and the output (y)
`approaches x.
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`Chap.1
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`Adaptive Systems
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`The adaptive predictor diagram in Figure 1.5(a) is redrawn in Figure 1.6, with
`examples of several conventionsof notation that are used throughoutthis text. The
`symbols x,, y,, and e, represent the kth elementsin the time series represented by
`x, y, and e. Usually, the time series may be assumed to be obtained by sampling
`continuous signals. Thus x, = x(kT), and so on, where T is the time step or
`interval between samples. The symbol z~™ standsfor a fixed delay of M timesteps,
`so that in Figure 1.6 the output of the z~™ blockis labeled x,_,,. The symbol H,
`represents the transfer characteristic of the adaptive processor or “adaptivefilter.”
`Weleave a detailed description of H, to subsequent chapters, except to note here
`that the subscript k indicates that the transfer characteristic possibly changes at
`each sample point.
`Thus in Figure 1.6 wesee that the input signal, x,, is delayed and then filtered
`to produce y,, and that y, is subtracted from x,
`to obtain the error, e,. The
`transfer function, H,, is adjusted to keep the average squared value ofthis error as
`small as possible. In this way, the processor always uses past values of x to predict
`the present value of x while using e to adjust H, and is thus involved in a
`performance-feedback process.
`An example of adaptive predictor performance is shown in Figure 1.7. The -
`waveformsare constructed from digital data (here as well as in examples ahead) by ghee few
`drawing straight line>between the sample points. The input, x, is a frequency-limite
`.
`random signal, and M = 1 in this case. Note that y, becomes a better prediction of
`x,, and that the magnitudeof e, decreases, as k increases and the adaptive system
`learns progressively to predict x,. More detailed examples of adaptive prediction
`are covered in subsequent chapters.
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`4
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`THE CHAPTERS AHEAD
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`In Chapters 2 through 8 we present some basic discussion and mathematical
`description of the adaptive process. The performance of adaptive systems can be
`analyzed either in the time domain or in the frequency domain; in general,
`the
`frequency-domain analysis tends to be more elegant and difficult. Therefore, in
`Chapters 2 through 6 we stay in the time domain and avoid using transforms,
`transfer functions, and so on, as much as possible. In Chapter 2 we introduce the
`adaptive linear combiner, whichis the basic nonrecursive form of the adaptivefilter.
`Then in Chapters 3 through 5 we introduce the geometry of the “performance
`surface” and consider various methodsof adaptively seeking the minimum point on
`this surface.
`In Chapter6 we introduce the well-known least-mean-square (LMS)algorithm,
`which is the simplest, most important, and most widely used algorithm for adjusting
`the weights in a linear adaptive system. After reviewing Chapter 2,
`the more
`advanced reader or the reader wishing simply to apply the LM