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`UNITED STATES PATENT AND TRADEMARK OFFICE
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`BEFORE THE PATENT TRIAL AND APPEAL BOARD
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`APPLE INC.,
`Petitioner,
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`v.
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`ANDREA ELECTRONICS INC.,
`Patent Owner.
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`Patent No. 6,363,345
`Issued: March 26, 2002
`Filed: February 18, 1999
`
`Inventors: Joseph Marash, et al.
`Titles: SYSTEM, METHOD, AND APPARATUS FOR CANCELLING NOISE
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`IPR2017-00627
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`DECLARATION OF BERTRAND HOCHWALD REGARDING U.S.
`PATENT NO. 6,363,345
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`
`
`Petitioner Apple Inc.
`Ex. 1004, p. i
`
`

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`IPR2017-00627
`
`Declaration of Dr. Bertrand Hochwald
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`I.
`
`TABLE OF CONTENTS
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`INTRODUCTION ......................................................................................... 1
`A.
`Engagement ........................................................................................... 1
`B.
`Background and Qualifications ............................................................. 1
`C.
`Compensation and Prior Testimony ...................................................... 4
`D.
`Information Considered ......................................................................... 4
`LEGAL STANDARDS FOR PATENTABILITY ...................................... 5
`II.
`A. Anticipation ........................................................................................... 6
`B.
`Obviousness ........................................................................................... 7
`III. BACKGROUND INFORMATION ABOUT THE ’345 PATENT........... 9
`A.
`Effective Filing Date of the ’345 Patent ............................................... 9
`B.
`The Prosecution History of The ’345 Patent ......................................... 9
`C.
`Technical Field .................................................................................... 10
`D.
`Level of Ordinary Skill in the Art ....................................................... 10
`IV. TECHNICAL BACKGROUND ................................................................. 11
`A. Digital Audio Signals .......................................................................... 11
`B.
`Signal Processing ................................................................................ 14
`C.
`Filtering ............................................................................................... 22
`D.
`Spectral Subtraction ............................................................................ 23
`V. ANALYSIS OF THE ’345 PATENT ......................................................... 26
`A. Overview of the ’345 Patent ................................................................ 26
`1. Boll Summary ............................................................................... 27
`2. Improvements to Boll (1979) prior to Filing of ’345 Patent......... 29
`3. The ’345 Patent’s Purported Improvements to Boll ..................... 31
`B.
`Construction of Terms Used in the ’345 Patent Claims ...................... 34
`1. Background on the Broadest Reasonable Interpretation ............... 34
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`Petitioner Apple Inc.
`Ex. 1004, p.ii
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`

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`IPR2017-00627
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`C.
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`Declaration of Dr. Bertrand Hochwald
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`2. Broadest Reasonable Interpretation of Terms of the ’345
`Patent ............................................................................................. 35
`a) “magnitude” (claims 1, 38) .................................................... 35
`b) “frequency spectrum generator” / ”generating the frequency
`spectrum” (claims 1, 38) ........................................................ 36
`c) “threshold detector for setting a threshold… and for
`detecting” (claim 1) ................................................................ 36
`d) “generating a noise canceling signal for canceling noise” ..... 36
`e) “current minimum value” (claims 4, 6, 8, 10-11, 39) ............ 37
`f) “future minimum value” (claims 4-7, 9, 39-41) ..................... 38
`VI.
`IDENTIFICATION OF THE PRIOR ART ............................................. 39
`VII. ANALYSIS OF THE PRIOR ART AND ’345 CLAIMS ........................ 40
`A. Helf ...................................................................................................... 40
`1. Helf Describes the Elements of Claims 1-3, 13-14, 21, 23,
`and 38 of the ’345 Patent .............................................................. 44
`2. Helf Describes the Elements of Claims 4-7, 9-11, 39-41,
`and 43-45 of the ’345 Patent ......................................................... 50
`B. Martin .................................................................................................. 55
`1. Overview of Martin ....................................................................... 55
`2. Martin Describes the Elements of Claims 4-11 and 39-41 of
`the ’345 Patent ............................................................................... 57
`3. A Person of Ordinary Skill Would Have Considered Helf
`and Martin Together ...................................................................... 64
`4. Helf and Martin Render Claims 6, 8, 9, 12, 25, 42, and 46
`Obvious ......................................................................................... 65
`5. Helf and Martin Render Claims 25 and 46 of the ’345
`Patent Obvious .............................................................................. 70
`Boll ...................................................................................................... 70
`1. Overview of Boll ........................................................................... 70
`2. A Person of Ordinary Skill Would Have Considered Helf
`and Boll Together .......................................................................... 71
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`Petitioner Apple Inc.
`Ex. 1004, p.iii
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`3. Helf and Boll Render Claims 17-20 and 47 of the ’345
`Patent Obvious .............................................................................. 72
`D. Additional Combinations .................................................................... 74
`1. Other References ........................................................................... 74
`a) Overview of Arslan ................................................................ 74
`b) Overview of Uesugi ................................................................ 77
`2. Helf and Arslan: Claims 15 and 16 ............................................... 78
`3. Helf, Boll, and Arslan: Claim 24 .................................................. 79
`4. Helf, Martin, and Uesugi ............................................................... 80
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`Petitioner Apple Inc.
`Ex. 1004, p.iv
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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`I.
`
`INTRODUCTION
`A. Engagement
`1.
`I have been retained by counsel for Apple Inc. as an expert witness in
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`the above-captioned proceeding. I have been asked to provide an opinion
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`regarding the patentability of certain claims in U.S. Patent No. 6,363,345
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`(“the ’345 Patent”) (Exhibit 1001). I have been asked to provide a discussion of
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`the meaning of certain words and phrases in the claims of the ’345 patent, to
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`provide a description of state of the art of the technology described in the ’345
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`patent, and to analyze various references that I understand are prior art to these
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`patents.
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`B.
`2.
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`Background and Qualifications
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`In 1995 I received a Ph.D. in Electrical Engineering from Yale
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`University. My PhD work involved the analysis and processing of electromagnetic
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`and audio signals for the estimation of the location of electromagnetic and audio
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`sources. In 1993 I received an M.A. in Statistics from Yale University. My
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`primary area of study was Statistical Signal Processing. I received an M.S. in
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`Electrical Engineering from Duke University in 1986, and a B.S. in Engineering
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`from Swarthmore College in 1984.
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`3.
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`I have twenty years of combined industry and academic experience in
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`the research and design of systems for signal processing, and wireless and wireline
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`communications.
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`Petitioner Apple Inc.
`Ex. 1004, p.1
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`4. My most recent appointment, starting in 2011, is with the University
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`of Notre Dame, where I am currently a Freimann Chaired Professor of Electrical
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`Engineering. I teach both graduate and undergraduate classes in Communication
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`Systems and in Signals and Systems, where the emphasis is on the processing of
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`analog and digital signals. My primary areas of research include communication
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`systems, radio-frequency circuits, and signal design and processing. I advise
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`graduate students who are attaining Ph.D. degrees through research and
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`coursework.
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`5.
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`Prior to Notre Dame, I worked from 2005-2010 at Beceem
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`Communications, a cellular wireless communication chipset start-up company in
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`Santa Clara, California, where I was Chief Scientist and Vice President of Systems
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`Engineering. I was an integral part of the chipset development team. Beceem was
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`bought by Broadcom Corporation in 2010 and no longer exists as a separate
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`company.
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`6.
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`Prior to Beceem, I worked from 1996-2005 at Lucent Bell
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`Laboratories in New Jersey, where I was as a Distinguished Member of the
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`Technical Staff doing research into communications systems and multiple-antenna
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`systems. As a result of my research, I obtained many patents and wrote numerous
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`publications across a variety of areas in communication theory, information theory,
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`and circuit design.
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`Petitioner Apple Inc.
`Ex. 1004, p.2
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`7.
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`Prior to Bell Laboratories, I was a Visiting Assistant Professor at the
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`University of Illinois in Urbana-Champaign during the 1995-1996 school year,
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`where I worked on a broad range of research topics related to signal processing and
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`communications.
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`8.
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`Prior to completing my Ph.D., during 1986-1989 I worked at the
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`Department of Defense as a system engineer for signal processing and wireless
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`communication systems. In this job I designed communication equipment for the
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`sampling, filtering and processing of audio signals.
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`9.
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`I have published approximately 95 articles in scholarly journals, many
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`of them within the journals of the Institute of Electrical and Electronic Engineers
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`(IEEE), one of the premier societies for electrical engineers. I have been an invited
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`and plenary speaker at several international conferences throughout the world and
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`have received awards and recognition for my research and publications.
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`10.
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`I have 45 granted patents in a variety of areas related to
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`communication and signal processing systems. I have had experience drafting and
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`successfully prosecuting my own patents, and have worked with other experts in
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`signal processing systems as a co-inventor and co-author.
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`11.
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`In addition to my academic and practical experience, I have worked as
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`an expert in the areas of communication and signal processing systems, as detailed
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`in Exhibit A, attached to the end of this declaration.
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`Petitioner Apple Inc.
`Ex. 1004, p.3
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`12. A copy of my CV has been attached as Exhibit B.
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`C. Compensation and Prior Testimony
`13.
`I am being compensated for my time at the rate of $600 per hour for
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`my work in connection with this matter. I am being reimbursed for reasonable and
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`customary expenses associated with my work in this investigation. This
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`compensation is not dependent in any way on the contents of this Declaration, the
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`substance of any further opinions or testimony that I may provide or the ultimate
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`outcome of this matter.
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`14. Within the last five years, I have testified by deposition in: Airvana v.
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`Ericsson. I have also testified at Andrea Electronics v. Lenovo. I also submitted
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`declarations in IPR2016-00459, IPR2016-00461, and IPR2016-00474 on behalf of
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`Waves Audio.
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`D.
`Information Considered
`15. My opinions are based on my years of education, research, and
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`experience, as well as my investigation and study of relevant materials. In forming
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`my opinions, I have considered the materials I identify in this report and those
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`listed in the Exhibit List included with the petition.
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`16.
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`I may rely upon these materials and/or additional materials to respond
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`to arguments raised by the Patent Owner. I may also consider additional
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`Petitioner Apple Inc.
`Ex. 1004, p.4
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`documents and information in forming any necessary opinions—including
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`documents that may not yet have been provided to me.
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`17. My analysis of the materials produced in this investigation is ongoing,
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`and I will continue to review any new material as it is provided. This report
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`represents only those opinions I have formed to date. I reserve the right to revise,
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`supplement, and/or amend my opinions stated herein based on new information
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`and on my continuing analysis of the materials already provided.
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`II. LEGAL STANDARDS FOR PATENTABILITY
`18. Certain basic legal principles have been explained to me by counsel
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`for Apple. Below, I have recorded these legal standards as they were explained to
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`me.
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`19.
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`I understand that for an invention claimed in a patent to be found
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`patentable, it must be, among other things, new and not obvious from what was
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`known before the invention was made.
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`20.
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`I understand the information that is used to evaluate whether an
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`invention is new and not obvious is generally referred to as “prior art” and can
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`include patents and printed publications. I also understand that a patent will be
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`prior art if it was filed before the earliest effective filing date of the claimed
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`invention, while a printed publication will be prior art if it was publicly available
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`Petitioner Apple Inc.
`Ex. 1004, p.5
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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`before that date. I understand that in this proceeding, the information that may be
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`evaluated to show unpatentability is limited to patents and printed publications.
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`21.
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`I understand that in this proceeding Apple has the burden of proving
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`that the challenged claims are unpatentable over the prior art by a preponderance of
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`the evidence. I understand that “a preponderance of the evidence” is evidence
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`sufficient to show that a fact is more likely true than it is not.
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`22.
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`I understand that there are two ways in which prior art may render a
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`patent claim unpatentable. First, the prior art can be shown to “anticipate” the
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`claim. Second, the prior art can be shown to have made the claim “obvious” to a
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`person of ordinary skill in the art.
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`A. Anticipation
`23.
`I understand that, for a patent claim to be “anticipated” by the prior art,
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`each and every requirement of the claim must be found, expressly or inherently, in
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`a single prior art reference as recited in the claim.
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`24.
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`I understand that claim limitations that are not expressly described in
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`a prior art reference may still be there if they are “inherent” to the thing or process
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`being described in the prior art.
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`25.
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`I understand that it can be acceptable to consider evidence other than
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`the information in a particular prior art document to determine if a feature is
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`necessarily present in or inherently described by that document.
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`Petitioner Apple Inc.
`Ex. 1004, p.6
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`26.
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`I understand that if a reference incorporates other documents by
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`reference, the incorporating reference and the incorporated reference(s) should be
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`treated as a single prior art reference for purposes of analyzing anticipation.
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`27.
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`I understand that to be anticipatory, a reference must not only
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`explicitly or inherently disclose every claimed feature, but those features must also
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`be “arranged as in the claim.” Differences between the prior art reference and a
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`claimed invention, however slight, invoke the question of obviousness, not
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`anticipation.
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`B. Obviousness
`28.
`I understand that a claimed invention is not patentable if it would have
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`been obvious to a person of ordinary skill in the field of the invention at the time
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`the invention was made. I understand that in determining whether a patent claim is
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`obvious, one must consider the following four factors: (i) the scope and content of
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`the prior art, (ii) the differences between the prior art and the claims at issue, (iii)
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`the knowledge of a person of ordinary skill in the pertinent art; and (iv) objective
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`factors indicating obviousness or non-obviousness, if present (such as commercial
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`success or industry praise).
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`29.
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`I understand the objective factors indicating obviousness or non-
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`obviousness may include: commercial success of products covered by the patent
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`claims; a long-felt need for the invention; failed attempts by others to make the
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`Petitioner Apple Inc.
`Ex. 1004, p.7
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`invention; copying of the invention by others in the field; unexpected results
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`achieved by the invention; praise of the invention by those in the field; the taking
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`of licenses under the patent by others; expressions of surprise by experts and those
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`skilled in the art at the making of the invention; and the patentee proceeded
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`contrary to the accepted wisdom of the prior art. I also understand that any of this
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`evidence must be specifically connected to the invention rather than being
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`associated with the prior art or with marketing or other efforts to promote an
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`invention. I am not presently aware of any evidence of “objective factors”
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`suggesting the claimed methods are not obvious, and reserve my right to address
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`any such evidence if it is identified in the future.
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`30.
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`In addition, I understand that the obviousness inquiry should not be
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`done in hindsight, but must be done using the perspective of a person of ordinary
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`skill in the relevant art as of the effective filing date of the patent claim.
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`31.
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`I understand that the Supreme Court has rejected a rigid approach to
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`determining the question of obviousness, such as one that requires a challenger to
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`identify a “teaching, suggestion, or motivation to combine” known elements.
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`Instead, a challenger needs to articulate reasoning for combining known elements.
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`Such reasoning can be based on design considerations, market demands, looking to
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`solutions to related problems in related fields, and on the “ordinary innovation”
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`and creativity that would be applied by a person of ordinary skill in the art.
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`Petitioner Apple Inc.
`Ex. 1004, p.8
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`32.
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`I understand that an invention that might be considered an obvious
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`variation or modification of the prior art may be considered non-obvious if one or
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`more prior art references discourages or leads away from the line of inquiry
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`disclosed in the reference(s). A reference does not “teach away” from an invention
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`simply because the reference suggests that another embodiment of the invention is
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`better or preferred. My understanding of the doctrine of teaching away requires a
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`clear indication that the combination should not be attempted (e.g., because it
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`would not work or explicit statements saying the combination should not be made).
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`III. BACKGROUND INFORMATION ABOUT THE ’345 PATENT
`A. Effective Filing Date of the ’345 Patent
`33. The ’345 patent issued from Application No. 09/252,874 filed on
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`February 18, 1999. It does not claim the benefit of priority to any other application.
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`Accordingly, it is my understanding that the effective filing date of the ’345 patent
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`claims is no earlier than February 18, 1999.
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`B.
`34.
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`The Prosecution History of The ’345 Patent
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`I understand that the ’345 patent claims were initially rejected under
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`the following grounds: (1) failure to submit a legible IDS, (2) obviousness-type
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`double patenting, and (3) being indefinite or not enabled. [’345 file history.
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`(Exhibit 1002)] Following the submission of additional documentation, the
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`Examiner withdrew rejections (1)-(2). [’345 file history]. After Patent Owner
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`Petitioner Apple Inc.
`Ex. 1004, p.9
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`amended the claims, the Examiner withdrew the § 112 rejection and allowed them.
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`[’345 file history].
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`C. Technical Field
`35. The ’345 disclosure generally relates to digital signal processing
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`techniques that are used to reduce the noise present in an audio speech signal [‘345,
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`Abstract (Exhibit 1001)].
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`D. Level of Ordinary Skill in the Art
`36.
`I have been instructed that the claims of a patent are to be reviewed
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`from the point of view of a hypothetical person of ordinary skill in the art at the
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`time of the filing of the patent.
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`37.
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`I believe a person of ordinary skill in the art in the field of the ’345
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`patent in February 1999 would have been someone with a good working
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`knowledge of digital signal processing techniques and their applications. The
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`person would have gained this knowledge through an undergraduate education in
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`electrical engineering or a comparable field, in combination with either a graduate
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`degree (or two years of graduate work) in electrical engineering or a comparable
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`field, or through two years of practical work experience, where such graduate
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`education or work experience focused on or involved the use of digital signal
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`processing techniques.
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`Petitioner Apple Inc.
`Ex. 1004, p.10
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`38.
`
`In preparing this declaration, I have considered the issues from the
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`perspective of a hypothetical person of ordinary skill in the art on February 18,
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`1999.
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`IV. TECHNICAL BACKGROUND
`A. Digital Audio Signals
`39. What humans perceive as sound is the physical vibrations of air (or
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`another medium, such as water). For example, when a string on a musical
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`instrument is played, the string vibrates and causes the air nearby to oscillate in
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`responses. The oscillation propagates through the air, attenuating with distance.
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`The oscillation of the air can be detected by the ear drum, which humans perceive
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`as a sound [Deller et al., Discrete-Time Processing of Speech Signals, at 99-101
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`(Deller is Exhibit 1012)].
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`40. An audio signal is a representation of sound. A standard graphical
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`representation of the audio signal is a sinusoidal wave, with time on the x-axis, and
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`signal amplitude on the y-axis [Oppenheim and Willsky, Signals and Systems,
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`Prentice Hall, 1979, at pg. 16 (Oppenheim is Exhibit 1014)].
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`Petitioner Apple Inc.
`Ex. 1004, p.11
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`
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`This graph depicts the oscillation of the air over time. This is referred as being a
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`time domain representation of the sound. In other words, the x-axis represents
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`time.
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`41. Two of the properties of a sound wave that are particularly relevant to
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`human hearing are its amplitude and frequency. Amplitude refers to how tall or
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`high along the y-axis the signal is, and it roughly corresponds to how loud the
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`sound would be. A tall wave is loud, while a small wave along the y-axis is quiet.
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`The size of a sound wave is measured in decibels (dB). A conversation is
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`considered at normal levels if the speech level at the listeners is 60 dB.
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`42. Frequency refers to how quickly the signal oscillates and corresponds
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`to the pitch of the sound (or the musical note). A slowly oscillating wave creates a
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`low-pitched noise, while a quickly oscillate wave creates a high-pitched noise.
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`Frequency is measure in Hertz (Hz), which means cycles per second. In the figure
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`above, if the x-axis represents one second of time, then approximately three cycles
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`Petitioner Apple Inc.
`Ex. 1004, p.12
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`occur in one second, representing a 3 Hz signal. Normal human hearing is
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`sensitive to signals in the range of 20 Hz to 20,000 Hz. A 20 Hz signal
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`corresponds to a very low tone, and a 20,000 Hz represents a very high one.
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`43.
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`In digital signal processing an analog signal is converted into a digital
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`representation of the signal by “sampling” the signal. A sample is the amplitude of
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`the wave at a particular point in time. This process is illustrated below. The red
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`line represents the audio signal and each blue dot represent a single sample.
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`The result is that the computer stores a set of points that represent the continuous
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`audio signal.
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`
`
`Petitioner Apple Inc.
`Ex. 1004, p.13
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`
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`To ensure that the digital samples accurately reflect the sound wave, the samples
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`must be collected at least twice the rate of the highest frequency in the signal. So
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`if the audio signal includes frequencies up to 8000 Hz, the samples must be
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`collected at 16000 Hz (16000 samples per second) or higher.
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`B.
`Signal Processing
`44. Music, human speech, and many other human perceptible noises are
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`sounds comprising combinations of sound waves of several different frequencies.
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`For example, a musical chord is several notes played at the same time, contributing
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`to the “richness” of the sound. The resulting signal does not necessarily look
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`sinusoidal anymore.
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`Petitioner Apple Inc.
`Ex. 1004, p.14
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`
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`The example in the figure above shows a signal that is actually a composite of
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`several different sinusoidal waves, each corresponding to an individual frequency
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`and amplitude. The resulting signal is not sinusoidal but still has a repetitive
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`appearance. The above example is an approximation of a square wave (which is
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`not a speech signal).
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`45. These figures depict the evolution of the sound wave over time. Just
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`from looking at the figures, it is difficult to tell which frequencies are present in the
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`signal. However, using a well-known mathematical formula called the “Fourier
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`transform”, the sound wave can be separated into its individual frequency
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`components. Typically, the signal is divided into a set of short frames, and the
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`frequency components in each frame can be extracted using the Fourier transform.
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`In digital signal processing, typically a Fast Fourier Transform (FFT) or a Discrete
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`Fourier Transform (DFT) is used for reasons of speed or processing efficiency.
`
`Petitioner Apple Inc.
`Ex. 1004, p.15
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`

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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`46. Performing a Fourier transform on a sound wave changes the wave
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`from the time domain (where you can see how the amplitude changes over time) to
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`the frequency domain (where you can see for example the magnitude of the
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`different frequencies in the sound). In the frequency domain, a graph of the audio
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`signal often looks like a histogram. The signal is divided into “frequency bins”
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`where each bin corresponds to one of the frequencies present in the signal. The
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`index of each frequency bin (x-axis in the figure below) corresponds to the
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`frequency, and the magnitude in that bin (y-axis) can be thought of as the
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`magnitude (which is the absolute value of its amplitude) of the signal at that
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`frequency.
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`47. Typically the value that the Fourier transform puts into the frequency
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`bin is a complex number. A complex number is a number that has two
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`
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`Petitioner Apple Inc.
`Ex. 1004, p.16
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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`components: a real component and an imaginary component. In the figure below
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`the x-axis is labeled “Re” for “real” and the y-axis is labeled “Im” for “imaginary”.
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`
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`The complex number is indicated on this figure by the black circle in the
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`upper right. Hence, the complex number is expressed as the pair (x,y), where “x”
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`
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`is the real portion and “y” is the imaginary portion.
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`48. Another way to represent the complex number (x, y) is using the pair
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`(r, (cid:2030)), where “r” is the magnitude of the complex number and “(cid:2030)” is the phase.
`shows the (r, (cid:2030)) representation. This representation is entirely equivalent to the
`connecting the (x,y) representation and (r,(cid:2030)) representation are
`(cid:1870)=(cid:3493)(cid:1876)(cid:2870)+(cid:1877)(cid:2870)
`(cid:2030)=tan(cid:2879)(cid:2869)(cid:4672)(cid:3052)(cid:3051)(cid:4673)
`49. The (r,(cid:2030)) representation is useful because when the Fourier transform
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`This representation can be referred to as polar coordinates. The above figure also
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`(x,y) representation but is perhaps more intuitive for the purposes of analyzing a
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`frequency bin, and hence I will focus on this representation. The formulas
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`
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`of a sinusoid signal with frequency f is taken, the magnitude r of the complex
`Petitioner Apple Inc.
`Ex. 1004, p.17
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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`frequency f contained in the original audio signal. The phase (cid:2030) of the complex
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`number stored in frequency bin f gives the magnitude of the sinusoid with
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`number stored in the frequency bin gives the phase of the sinusoid in the original
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`audio signal. The phase relates to the starting point of the sinusoidal signal. The
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`two signals below have different phases but are perceived by the ear as the same
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`tone at the same loudness.
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`50. Like other signals, an audio signal can be converted between the time
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`and frequency domains using a Fourier transform. The audio signal is divided into
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`short frames, and then an FFT is applied to each frame. The FFT segments the
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`audio signal into its individual frequencies, measures the magnitude of each, and
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`the result is the frequency domain representation. The function has an inverse,
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`allowing the frequency domain representation to be converted back into the time
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`domain. This process is illustrated below.
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`Petitioner Apple Inc.
`Ex. 1004, p.18
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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`The above figure is taken from Wikipedia,1 and I have added annotations.
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`51. The signal shown above is for the purpose of illustrating the Fourier
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`transform process, and the signal depicted does not correspond to a typical audio
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`signal. The shape of speech and sound signals can vary substantially over time.
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`Examples of signals reflecting simple speech sounds are shown in the time domain
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`in the center of the figure below, with the corresponding frequency domain
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`representation on the right.
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`1 https://en.wikipedia.org/wiki/Frequency_domain
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`Petitioner Apple Inc.
`Ex. 1004, p.19
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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`[Deller et al., Discrete-Time Processing of Speech Signals, at 123, 135.] As can be
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`seen from the frequency domain representation, in the figure above, the top
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`signal’s primary frequency components are 900 Hz, 2.5 kHz, and 3.5 kHz, while
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`the bottom signal is mostly a 1 kHz signal.
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`52.
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`If a signal is a pure 1000 Hz tone stretching for all time without any
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`beginning or end, then it has a single frequency component at 1000 Hz. A Fourier
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`transform of this signal reveals the 1000 Hz component, with all the remaining
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`components being zero. If a signal is initially silent then comprises a pure 1000 Hz
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`tone and is then silent again, taking its Fourier transform (which includes the silent
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`portions) reveals frequency components in addition to the 1000 Hz tone. These
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`additional frequency components act to “turn on” and “turn off” the signal. Since
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`speech and most signals that are processed necessarily have a beginning and an end,
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`Fourier processing of such signals therefore produces frequency “artifacts”,
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`relevant to the short duration of these signals but not directly relevant to the signal
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`itself. It is generally desired to mitigate these artifacts by making the processing
`Petitioner Apple Inc.
`Ex. 1004, p.20
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`IPR2017-00627
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`Declaration of Dr. Bertrand Hochwald
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`blocks as long as possible. But since processing blocks are necessarily limited,
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`“windows” are also used, whose actions multiply the signals and soften, or taper,
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`the effects of the beginning and end of the signal. An example of such a window is
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`the “Hanning” window.
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`53. Because of the taper in the Hanning window, some of the signal at the
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`edges of the processing block of an audio segment are attenuated and made small.
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`In order to properly process these edge signals, it is then advantageous to “slide the
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`window” so that the trai