Table Of ContentThe Theory of Linear Prediction
Copyright© 2008byMorgan&Claypool
Allrightsreserved.Nopartofthispublicationmay bereproduced, storedinaretrievalsystem, ortransmittedin
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TheTheoryofLinearPrediction
P.P.Vaidyanathan
www.morganclaypool.com
ISBN:1598295756 paperback
ISBN:9781598295757 paperback
ISBN:1598295764 ebook
ISBN:9781598295764 ebook
DOI:10.2200/S00086ED1V01Y200712SPR03
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONSIGNALPROCESSING#3
Lecture#3
SeriesEditor:JoséMoura,CarnegieMellonUniversity
SeriesISSN
ISSN1932-1236 print
ISSN1932-1694 electronic
The Theory of Linear Prediction
P.P.Vaidyanathan
CaliforniaInstituteofTechnology
SYNTHESISLECTURESONSIGNALPROCESSING#3
M
&C &
Morgan Claypool Publishers
ToUsha,Vikram,andSagarandmyparents.
vi
ABSTRACT
Linear prediction theory has had a profound impact in the field of digital signal processing.
Although the theory dates back to the early 1940s, its influence can still be seen in applications
today.The theoryis basedon very elegantmathematicsand leadstomany beautifulinsightsinto
statisticalsignalprocessing.Although predictionisonlyapartofthemoregeneraltopicsoflinear
estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled
detailed discussionof a number of issues that are normally not found in texts. For example, the
theory of vector linear prediction is explained in considerable detail and so is the theory of line
spectralprocesses.Thisfocusanditssmallsizemakethebookdifferentfrommanyexcellenttexts
which cover the topic, including a few that are actually dedicatedto linear prediction. There are
several examples and computer-baseddemonstrationsof the theory. Applications are mentioned
whereverappropriate,but thefocusisnoton thedetaileddevelopmentoftheseapplications.The
writing style is meant to be suitable for self-studyas well as for classroom use at the senior and
first-yeargraduatelevels.Thetextisself-containedforreaderswithintroductoryexposuretosignal
processing,randomprocesses,andthetheoryofmatrices,andahistoricalperspectiveanddetailed
outlinearegiveninthefirstchapter.
KEYWORDS
Linearpredictiontheory,vectorlinearprediction,linearestimation,filtering,smoothing,
linespectralprocesses,Levinson’srecursion,latticestructures,autoregressivemodels
vii
Preface
Linear prediction theory has had a profound impact in the field of digital signal processing.
Although the theory dates back to the early 1940s, its influence can still be seen in applications
today.The theoryis basedon veryelegant mathematicsand leadsto many beautifulinsightsinto
statisticalsignalprocessing.Although predictionisonlyapartofthemoregeneraltopicsoflinear
estimation, filtering, and smoothing, I have focused on linear prediction in this book. This has
enabledmetodiscussindetailanumberofissuesthatarenormallynotfoundintexts.Forexample,
the theory of vector linear prediction is explained in considerable detail and so is the theory of
linespectralprocesses.Thisfocusanditssmall sizemakethe bookdifferentfrommany excellent
textsthatcoverthetopic,includingafewthatareactuallydedicatedtolinearprediction.Thereare
several examples and computer-baseddemonstrationsof the theory. Applications are mentioned
whereverappropriate,butthefocusisnotonthedetaileddevelopmentoftheseapplications.
The writing style is meant to be suitable for self-studyas well as for classroom use at the
seniorandfirst-yeargraduatelevels.Indeed,thematerialhereemergedfromclassroomlecturesthat
I hadgiven overthe yearsatthe CaliforniaInstituteofTechnology.So,the text isself-contained
for readers with introductory exposure to signal processing, random processes,and the theory of
matrices.AhistoricalperspectiveandadetailedoutlinearegiveninChapter1.
ix
Acknowledgments
The pleasant academic environment provided by the California Institute of Technology and the
generous support from the National Science Foundation and the Office of Naval Research have
beencrucialindevelopingsomeoftheadvancedmaterialscoveredinthisbook.
During my ‘‘young’’ days, I was deeply influenced by an authoritative tutorial on linear
filtering by Prof. Tom Kailath (1974) and a wonderful tutorial on linear prediction by John
Makhoul (1975). These two articles, among other excellent references,have taught me a lot and
so has the book by Anderson and Moore (1979). My ‘‘love for linear prediction’’ was probably
kindledby thesethree references.The small contributionI have made here would not have been
possiblewereitnotforthesereferencesandotherexcellentonesmentionedintheintroductionin
Chapter1.
It is impossibleto reduceto wordsmy gratitudeto Usha, who has shown infinite patience
during my busy days with research and book projects. She has endured many evenings and
weekendsofmy ‘‘disappearance’’to work.Her sinceresupport and the enthusiasmandlove from
myuncomplainingsonsVikramandSagararemuchappreciated!
P.P.Vaidyanathan
CaliforniaInstituteofTechnology
