Table Of ContentSIGNAL
PROCESSING FOR
NEUROSCIENTISTS
SECOND EDITION
W D
IM VAN RONGELEN
ProfessorofPediatrics,Neurology,andComputationalNeuroscience,
TechnicalDirectorPediatricEpilepsyCenterResearchDirectorPediatricEpilepsyProgram
SeniorFellowComputationInstitute,TheUniversityofChicago,Chicago,IL,USA
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To Sebastiaan,Olivia, Simonne,Sofia,Micah, Solomon and Malachi
Preface to the Second Edition
This second edition of “Signal Processing for Neuroscientists”
includes the partly revised and updated material of the reprinted first
edition and its companion volume. At the request of my students,
colleagues, and readers, I have extended several chapters and added
new ones. As a result, this edition contains a few additional advanced
topics (the imaging section of Chapters 7, 8, and 13), an introduction to
differential equations and modeling dynamics (Chapters 9, 10, and 23),
and an overview of modeling activity of single neurons and neuronal
networks (Chapters 29 and 30). These last two chapters summarize
approaches to modeling of neural activity with a flavor of a historical
overview of modeling in neuroscience. Due to the review aspect of the
modeling component, these chapters include a much longer reference
list than the others. At multiple requests I have also included a series
of exercises with each chapter. Answers to a subset of these exercises
are available on http://booksite.elsevier.com/9780128104828/.
Overall, the end result of this second edition is fairly close to what I
hadinitiallyhopedtoproduceforthefirsteditionaboutadecadeagod
butcouldn’tfinishwithintheavailabletime.However,althoughthistext
appears much later than I had envisioned, I now have the additional
advantage of having taught the signal analysis and modeling topics
multipletimes todifferentgroupsofstudents,giving meamuchbetter
insight into how to present and explain the material. In addition, the
currenttext,figures,andexerciseswereextensivelyevaluatedandtested
by students and readers. Three years ago, some of the lectures were
madeavailableonYouTubeforaworldwideaudience,andthistriggered
usefulfeedbackandsuggestionsthatwereincludedinthisedition.The
overallgoalofthetextremainstopresentthemathematicalbackground
ofdifferenttypesofsignalanalysisandmodelinginneuroscience,andto
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illustrate this with practical examples in the form of MATLAB scripts
that are available on http://booksite.elsevier.com/9780128104828/.
Ultimately I hope this end result helps the reader when studying the
material in this text.
I want to include a few suggestions for those who plan to use this
text and/or its figures (http://booksite.elsevier.com/9780128104828/)
in their lectures. Most chapters are based on material and examples
that can be covered in a 1e1½h lecture. However, depending on the
background of the students, Chapters 9, 10, 15, 16, 21 and 22 may be
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combinedinsingle1½hlectures,whileChapters7and13,aswellasthe
overview in Chapter 30, are more suitable for multiple lectures of that
(cid:1)
length. In addition to the MATLAB material, some chapters also
include elements that can be used for lab sessions. A filter lab can be
based on the RC-circuit described in Chapter 15. For setting up more
advanced lab sessions, I describe membrane models using the integra-
te-and-fire circuit and the Nagumo equivalent circuit in Chapter 29
and Appendix 29.2.
Itisdifficulttothankeveryonewhocontributeddirectlyorindirectly
tothisbook,butIwilltry(withanapologytothoseIforgettoinclude).
InadditiontoallIalreadyacknowledgedinthepreviouseditionandits
companionvolume,IwanttothankmycollaboratorsattheUniversityof
Chicago and elsewhere: Drs. Michel J.A.M. van Putten, Stephan A. van
Gils, Catherine A. Schevon, Andrew K. Tryba, Charles J. Marcuccilli,
andJan-Marino(Nino)Ramirez.IalsothankDrs.StevenSmall,Ahmed
Shereen, and Justin Jureller for their critical input while writing
the material on imaging. Special thanks to Dr. Jack D. Cowan for
his inspiring guest lectures on the WilsoneCowan equations, and
who (in the many conversations we had) made me appreciate the
population model approach in neuroscience. I also thank my Teaching
AssistantsAlexSadovsky,ArupSarma,KylerBrown,AlbertWildeman,
James Goodman, Graham Fetterman, and Joe Dechery for their useful
suggestions. The feedback of the (under)graduate students, Mark
Saddler, Tahra Eissa, Jyothsna Suresh, Albert Wildeman, and Jeremy
Neuman, in my laboratory was very helpful. I also thank the people at
Elsevier, Dr. Natalie Farra, Kristi Anderson, and Poulouse Joseph for
their support and suggestions. Last but not least I thank Ingrid for her
ongoing fabulous support!
Preface to the Companion
Volume
This text is based on a course I teach at the University of Chicago
for students in Computational Neuroscience. It is a continuation of the
previously published text Signal Processing for Neuroscientists: An Intro-
duction to the Analysis of Physiological Signals and includes some of the
more advanced topics of linear and nonlinear systems analysis and
multichannel analysis. In the following, it is assumed that the reader is
familiar with the basic concepts that are covered in the introductory
text and, to help the student, multiple references to the basics are
included.
Thepopularityofsignalprocessinginneuroscienceisincreasing,and
with the current availability and development of computer hardware
andsoftwareitmaybeanticipatedthatthecurrentgrowthwillcontinue.
Because electrode fabrication has improved and measurement equip-
ment is getting less expensive, electrophysiological measurements
with large numbers of channels are now very common. In addition,
neuroscience has entered the age of light, and fluorescence measure-
ments are fully integrated into the researcher’s toolkit. Because each
image in a movie contains multiple pixels, these measurements are
multichannel by nature. Furthermore, the availability of both generic
and specialized software packages for data analysis has altered the
neuroscientist’s attitude toward some of the more complex analysis
techniques. Interestingly, the increased accessibility of hardware and
software may lead to a rediscovery of analysis procedures that were
initially described decades ago. At the time when these procedures
were developed, only few researchers had access to the required
instrumentation, but now most scientists can access both the necessary
equipment and modern computer hardware and software to perform
complex experiments and analyses.
The considerations given above have provided a strong motivation
for the development of this text, where we discuss several advanced
techniques, rediscover methods to describe nonlinear systems, and
examine the analysis of multichannel recordings. The first chapter
describestwoveryspecializedalgorithms:Lomb’salgorithmtoanalyze
unevenly sampled data sets and the Hilbert transform to detect
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instantaneous phase and amplitude of a signal. The remainder of the
text can be divided into two main components: (1) modeling systems
(Chapter 2) and the analysis of nonlinear systems with the Volterra
and Wiener series (Chapters 3e5) and (2) the analysis of multichannel
measurementsusingastatisticalapproach(Chapter6)andexamination
of causal relationships (Chapter 7). Throughout this text, we adopt
an informal approach to the development of algorithms and we
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include practical examples implemented in MATLAB . (All the
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MATLAB scripts used in this text can be obtained viahttp://www.
elsevierdirect.com/companions/9780123849151.)
Itisapleasuretoacknowledgethosewhohaveassisted(directlyand
indirectly)inthepreparationofthistext:Drs.V.L.Towle,P.S.Ulinski,D.
Margoliash, H.C. Lee, M.H. Kohrman, P. Adret, and N. Hatsopoulos.
I also thank the teaching assistants for their help in the course and in
the development of the material in this text: thanks, Matt Green, Peter
Kruskal, Chris Rishel, and Jared Ostmeyer. There is a strong coupling
between my teaching efforts and research interests. Therefore, I am
indebted to the Dr. Ralph and Marian Falk Medical Research Trust
for supporting my research and to the graduate and undergraduate
students in my laboratory: Jen Dwyer, Marc Benayoun, Amber Martell,
MuktaVaidya,andValeriyaTalovikova.Theyprovidedusefulfeedback,
tested some of the algorithms, and collected several example data sets.
Special thanks to the group of students in the 2010 winter class
who helped me with reviewing this material: Matt Best, Kevin Brown,
JonathanJui,MattKearney,LaneMcIntosh,JillianMcKee,LeoOlmedo,
Alex Rajan, Alex Sadovsky, Honi Sanders, Valeriya Talovikova, Kelsey
Tupper, and Richard Williams. Their multiple suggestions and critical
reviewhelpedtosignificantlyimprovethetextandsomeofthefigures.
AtElsevierIwanttothankLisaTickner,ClareCaruana,LisaJones,Mani
Prabakaran, and Johannes Menzel for their help and advice. Last but
not least, thanks to my wife Ingrid for everything and supporting the
multiple vacation days used for writing.
Preface to the First Edition
Thistextbookisanintroductiontosignalprocessingprimarilyaimedat
neuroscientists and biomedical engineers. The text was developed for a
one-quarter course I teach for graduate and undergraduate students at
theUniversityofChicagoandtheIllinoisInstituteofTechnology.Thepur-
poseofthecourseistointroducesignalanalysistostudentswithareason-
ablebutmodestbackgroundinmathematics(includingcomplexalgebra,
basiccalculus,andintroductoryknowledgeofdifferentialequations)and
a minimal background in neurophysiology, physics, and computer pro-
gramming. To help the basic neuroscientist ease into the mathematics,
thefirstchaptersaredevelopedinsmallsteps,andmanynotesareadded
tosupporttheexplanations.Throughoutthetext,advancedconceptsare
introduced whereneeded, and in the cases where details would distract
too much from the “big picture,” further explanation is moved to an
appendix.Mygoalsaretoprovidestudentswiththebackgroundrequired
tounderstandtheprinciplesofcommerciallyavailableanalysessoftware,
to allow them to construct their own analysis tools in an environment
such as MATLAB(cid:1),1 and to make more advanced engineering literature
accessible.Mostofthechaptersarebasedon90-minlecturesthatinclude
(cid:1)
demonstrations of MATLAB scripts. Chapters 7 and 8 contain material
from three to four lectures. Each chapter can be considered as a stand-
aloneunit.Forstudentswhoneedtorefreshtheirmemoryonsupporting
topics,Iincludereferencestootherchapters.Thefigures,equations,and
appendicesarealso referencedindependently by chapter number.
(cid:1)
TheCDthataccompaniesthistextcontainstheMATLAB scriptsand
severaldatafiles.Thesescriptswerenotdevelopedtoprovideoptimized
algorithmsbutserveasexamplesofimplementationofthesignalprocess-
(cid:1)
ingtaskathand.Foreaseofinterpretation,allMATLAB scriptsarecom-
mented;commentsstartingwith%providestructureandexplanationof
proceduresandthemeaningofvariables.Togainpracticalexperiencein
signal processing, I advise the student to actively explore the examples
and scripts included and worry about algorithm optimization later. All
(cid:1)
scriptsweredevelopedtoruninMATLAB (Version7)includingthetool-
boxesforsignalprocessing(Version6),imageprocessing(Version5),and
wavelets (Version 3). However, aside from those that use a digital filter,
theFourierslicetheorem,orthewavemenu,mostscriptswillrunwithout
1MATLAB(cid:1)isaregisteredtrademarkofTheMathWorks,Inc.
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these toolboxes. Ifthestudent hasaccesstoanoscilloscope andfunction
generator, the analog filter section (Chapter 10) can be used in a lab
context.ThecomponentsrequiredtocreatetheRCcircuitcanbeobtained
fromanyelectronics store.
Iwantto thank Drs.V.L.Towle, P.S.Ulinski,D.Margoliash,H.C.Lee,
andK.E.Hecoxfortheirsupportandvaluablesuggestions.MichaelCar-
rollwasagreathelpasTAinthecourse.Michaelalsoworkedontheorig-
inaltextinDenglish,andIwouldliketothankhimforallhishelpandfor
significantly improving the text. Also, I want to thank my students for
their continuing enthusiasm, discussion, and useful suggestions. Special
thanks to Jen Dwyer (student) for her suggestions on improving the
textandexplanations.ThankstothepeopleatElsevier,JohannesMenzel
(seniorpublishingeditor),CarlM.Soares(projectmanager),andPhilCar-
penter (developmental editor), for their feedback and help with the
manuscript.
Finally, although she isn’t very much interested in signal processing,
Idedicatethisbookto mywife forhersupport:heelergbedanktIngrid.
