Table Of ContentMulti-Pitch Estimation
Synthesis Lectures on Speech &
Audio Processing
Editor
B.H.Juang,GeorgiaTech
Multi-PitchEstimation
MadsGræsbøllChristensenandAndreasJakobsson
2009
DiscriminativeLearningforSpeechRecognition:TheoryandPractice
XiaodongHe,LiDeng
2008
LatentSemanticMapping:Principles&Applications
JeromeR.Bellegarda
2007
DynamicSpeechModels:Theory,Algorithms,andApplications
LiDeng
2006
ArticulationandIntelligibility
JontB.Allen
2005
Copyright© 2009byMorgan&Claypool
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedin
anyformorbyanymeans—electronic,mechanical,photocopy,recording,oranyotherexceptforbriefquotationsin
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Multi-PitchEstimation
MadsGræsbøllChristensenandAndreasJakobsson
www.morganclaypool.com
ISBN:9781598298383 paperback
ISBN:9781598298390 ebook
DOI10.2200/S000178ED1V01Y200903SAP005
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONSPEECH&AUDIOPROCESSING
Lecture#5
SeriesEditor:B.H.Juang,GeorgiaTech
SeriesISSN
SynthesisLecturesonSpeech&AudioProcessing
Print1932-121X Electronic1932-1678
Multi-Pitch Estimation
Mads Græsbøll Christensen
AalborgUniversity,Denmark
Andreas Jakobsson
LundUniversity,Sweden
SYNTHESISLECTURESONSPEECH&AUDIOPROCESSING#5
M
&C Morgan &cLaypool publishers
ABSTRACT
Periodicsignalscanbedecomposedintosetsofsinusoidshavingfrequenciesthatareintegermulti-
plesofafundamentalfrequency.Theproblemoffindingsuchfundamentalfrequenciesfromnoisy
observationsisimportantinmanyspeechandaudioapplications,whereitiscommonlyreferredto
aspitchestimation.Theseapplicationsincludeanalysis,compression,separation,enhancement,au-
tomatictranscriptionandmanymore.Inthisbook,anintroductiontopitchestimationisgivenand
anumberofstatisticalmethodsforpitchestimationarepresented.Thebasicsignalmodelsandasso-
ciatedestimationtheoreticalboundsareintroduced,andthepropertiesofspeechandaudiosignals
arediscussedandillustrated.Thepresentedmethodsincludebothsingle-andmulti-pitchestima-
torsbasedonstatisticalapproaches,likemaximumlikelihoodandmaximumaposteriorimethods,
filtering methods based on both static and optimal adaptive designs,and subspace methods based
ontheprinciplesofsubspaceorthogonalityandshift-invariance.Theapplicationofthesemethods
to analysis of speech and audio signals is demonstrated using both real and synthetic signals,and
their performance is assessed under various conditions and their properties discussed.Finally,the
estimators are compared in terms of computational and statistical efficiency, generalizability and
robustness.
KEYWORDS
estimation theory,spectral estimation,pitch estimation,pitch detection,fundamental
frequency estimation, statistical signal processing, order estimation, model selection,
audioprocessing,audioanalysis,musictranscription,speechprocessing,combfiltering,
subspacemethods,optimalfiltering
To Majbritt and Erik
and
to Ylva, Maja, Lina, Erik, and Olle.
ix
Contents
SynthesisLecturesonSpeech&AudioProcessing ...........................iii
Preface .................................................................xiii
SymbolsandNotation ....................................................xv
Abbreviations.......................................................... xvii
1 Fundamentals.............................................................1
1.1 Introduction ........................................................... 1
1.2 RelatedWork .......................................................... 2
1.3 SomeApplications...................................................... 3
1.4 SignalModels.......................................................... 6
1.5 CovarianceMatrixModel............................................... 12
1.6 SpeechandAudioSignals .............................................. 14
1.7 OtherSignalModels................................................... 18
1.8 ParameterEstimationBounds ........................................... 19
1.9 EvaluationofPitchEstimators .......................................... 22
2 StatisticalMethods ...................................................... 25
2.1 Introduction .......................................................... 25
2.2 MaximumLikelihoodEstimation........................................ 25
2.3 NoiseCovarianceMatrixEstimation ..................................... 27
2.4 WhiteNoiseCase ..................................................... 29
2.5 SomeMaximumAPosterioriEstimators.................................. 33
2.6 MAPModelandOrderSelection........................................ 38
2.7 FastMulti-PitchEstimation ............................................ 42
2.8 ExpectationMaximization .............................................. 44
2.9 AnotherRelatedMethod ............................................... 48
2.10 HarmonicFitting...................................................... 49
