Table Of ContentLecture Notes in Bioengineering
Kamran Kiasaleh
Biological
Signals
Classification
and Analysis
Lecture Notes in Bioengineering
More information about this series at http://www.springer.com/series/11564
Kamran Kiasaleh
Biological Signals
fi
Classi cation and Analysis
123
Kamran Kiasaleh
Department ofElectrical Engineering
TheUniversity of Texasat Dallas
Richardson, TX
USA
ISSN 2195-271X ISSN 2195-2728 (electronic)
Lecture Notesin Bioengineering
ISBN978-3-642-54878-9 ISBN978-3-642-54879-6 (eBook)
DOI 10.1007/978-3-642-54879-6
LibraryofCongressControlNumber:2015942236
SpringerHeidelbergNewYorkDordrechtLondon
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This book is dedicated to my beloved wife,
Tae,
and my children Brandon, Kristen, and
Alison.
I am forever indebted to my mother for her
endless support
and to my late father for his love
of knowledge.
Preface
Biological systems have been known for many decades to produce measurable
signals,whichoftenrevealnontrivialinformationabouttheunderlyingprocessesat
work. It is the hope of the scientific community that from the observation and
processing of various biologically-generated signals one can draw unambiguous
conclusions regarding the state of a biological system. This “state” is of outmost
importance to a variety of applications, including disease diagnosis and detection
oftheonsetofmanydeadlydiseases,includingheartattack,stroke,cancer,among
otherillnessesplaguingmankindtoday.Thistextwillmakeanattempttoshedlight
on the concept of signals and systems not only from the “man-made” perspective,
butalsofromtheangleofnature-madeorbiologically-madeviewpoint.Ultimately,
the goal of this text is to enable the reader to bring to bear the vast knowledge of
digitalsignalprocessingtotacklethebiologicalsignalsinordertoextractimportant
information of clinical value. To achieve this goal, one has to acquire a healthy
knowledge of non-biological signals and systems as well as signal processing
techniques before embarking on an endeavor that brings into focus the need for
somewhat different types of signal processing mechanisms, concerned with non-
stationarysignalsimpairedbynonlinearandevenchaoticeffects.Itistheintention
heretoenablethereadertoexaminebiologicalsignalsandsystemsfromthedigital
signal processing perspective while keeping an eye on some of the shortcomings
ofthesignalprocessingsystemsinusetoday,whichrelyheavilyonthe“linearity”
assumption (or approximation) in order to arrive at implementable architectures. It
isnoteworthythat,throughoutthistext,weusetheterm“biologicalsignals”torefer
to signals originating from a biological entity. Rather seamlessly, we use the
expression “biomedical signal processing” to refer to the signal processing tools
that one brings to bear to study the behavior of biological signals.
Although this text is intended for an introductory class on biomedical signal
processing for senior-level undergraduate or first-year graduate students, the text
can readily serve as a reference textbook for professionals in the field concerned
with the development of biomedical devices. To that end, many examples are
vii
viii Preface
providedwhereverpossibletohelpthepracticingengineerwhomaynotbefamiliar
withbiologicalsignalsandsystemsorapracticingbiologistwithsolidbackground
in the field of biology who may lack an engineering insight to enhance his or her
understanding of key concepts in signal processing.
Contents
1 Non-Biological Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Discrete- and Continuous-Time Determinist Signals . . . . . . . . . . 2
1.2.1 Sampling Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Upsampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.3 Downsampling and Decimation . . . . . . . . . . . . . . . . . . . 12
1.2.4 Anti-Aliasing Filter (AAF). . . . . . . . . . . . . . . . . . . . . . . 12
1.2.5 Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.6 Delta Modulation (DM). . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2.7 Sigma-Delta (Σ(cid:1)ΔÞ Modulation. . . . . . . . . . . . . . . . . . 20
1.3 Discrete- and Continuous-Time Random Signals . . . . . . . . . . . . 23
1.3.1 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.3.2 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . 34
1.3.3 Energy and Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
1.3.4 Ergodicity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
1.3.5 Power Spectrum Density (PSD) . . . . . . . . . . . . . . . . . . . 57
1.3.6 Signal Space Representation . . . . . . . . . . . . . . . . . . . . . 69
1.3.7 Mean-Square Sense Sampling Theorem. . . . . . . . . . . . . . 82
2 Linear and Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.1 Linear Systems Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.1.1 System Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.1.2 Response of Linear Systems to Random Signals. . . . . . . . 91
2.2 Response of Nonlinear Systems to Random Signals . . . . . . . . . . 104
2.2.1 Nonlinear Processing of Gaussian Signals . . . . . . . . . . . . 105
2.2.2 Nonlinear Processing of WSS Gaussian Processes . . . . . . 113
2.2.3 Output PSD of DM Devices with WSS
Gaussian Input. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
2.3 Systems with Signal + Noise. . . . . . . . . . . . . . . . . . . . . . . . . . 120
2.3.1 Signal-to-Noise Ratio (SNR) . . . . . . . . . . . . . . . . . . . . . 124
2.3.2 Matched and Optimum Filtering. . . . . . . . . . . . . . . . . . . 126
ix
x Contents
3 Biological Signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
3.1 Electrocardiogram (ECG). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
3.1.1 QRS Complex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
3.1.2 The P Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.1.3 The PR Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.1.4 The QRS Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.1.5 The ST Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
3.1.6 The T Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
3.2 Electroencephalogram (EEG). . . . . . . . . . . . . . . . . . . . . . . . . . 144
3.2.1 δ Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
3.2.2 θ Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
3.2.3 α Band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
3.2.4 β Band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
3.2.5 γ Band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
3.2.6 EEG Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
3.3 Electromyogram (EMG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
4 Signal Processing Methods for Biological Signals. . . . . . . . . . . . . . 175
4.1 Independence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
4.1.1 Uncorrelated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
4.1.2 Orthogonal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
4.2 Is It Gaussian?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
4.2.1 Kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
4.2.2 Entropy and Negentropy. . . . . . . . . . . . . . . . . . . . . . . . 180
4.2.3 Mutual Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
4.3 “Distance” Between Two PDFs . . . . . . . . . . . . . . . . . . . . . . . . 186
4.3.1 Kolmogorov-Smirnov (KS) Distance. . . . . . . . . . . . . . . . 187
4.3.2 Hellinger Distance (HD) . . . . . . . . . . . . . . . . . . . . . . . . 187
4.3.3 Kullback-Leibler (KL) Divergence . . . . . . . . . . . . . . . . . 188
4.4 Detection and Estimation Methods . . . . . . . . . . . . . . . . . . . . . . 200
4.4.1 Signal Detection Using Hypothesis Testing (HT) . . . . . . . 200
4.4.2 Specificity and Sensitivity. . . . . . . . . . . . . . . . . . . . . . . 208
4.4.3 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 238
4.4.4 Whittle Likelihood Test (WLT) . . . . . . . . . . . . . . . . . . . 252
4.4.5 Frequency Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 258
5 Signal Decomposition Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
5.1 Principle Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 277
5.2 Independent Component Analysis. . . . . . . . . . . . . . . . . . . . . . . 288
5.2.1 Infomax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
5.3 Wavelet Decomposition (WD) . . . . . . . . . . . . . . . . . . . . . . . . . 301
5.3.1 Short Term Fourier Transform (STFT) . . . . . . . . . . . . . . 302
5.3.2 Continuous WT (CWT). . . . . . . . . . . . . . . . . . . . . . . . . 314
5.3.3 Father Wavelet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
