Practical Biomedical Signal Analysis Using MATLAB® © 2012 by Taylor & Francis Group, LLC Series in Medical Physics and Biomedical Engineering Series Editors: John G Webster, Slavik Tabakov, Kwan-Hoong Ng Other recent books in the series: Physics for Diagnostic Radiology, Third Edition P P Dendy and B Heaton (Eds) Nuclear Medicine Physics J J Pedroso de Lima (Ed) Handbook of Photonics for Biomedical Science Valery V Tuchin (Ed) Handbook of Anatomical Models for Radiation Dosimetry Xie George Xu and Keith F Eckerman (Eds) Fundamentals of MRI: An Interactive Learning Approach Elizabeth Berry and Andrew J Bulpitt Handbook of Optical Sensing of Glucose in Biological Fluids and Tissues Valery V Tuchin (Ed) Intelligent and Adaptive Systems in Medicine Oliver C L Haas and Keith J Burnham A Introduction to Radiation Protection in Medicine Jamie V Trapp and Tomas Kron (Eds) A Practical Approach to Medical Image Processing Elizabeth Berry Biomolecular Action of Ionizing Radiation Shirley Lehnert An Introduction to Rehabilitation Engineering R A Cooper, H Ohnabe, and D A Hobson The Physics of Modern Brachytherapy for Oncology D Baltas, N Zamboglou, and L Sakelliou Electrical Impedance Tomography D Holder (Ed) Contemporary IMRT S Webb © 2012 by Taylor & Francis Group, LLC Series in Medical Physics and Biomedical Engineering K J Blinowska University of Warsaw, Poland J Zygierewicz University of Warsaw, Poland Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business A TA Y L O R & F R A N C I S B O O K © 2012 by Taylor & Francis Group, LLC MATLAB® and Simulink® are trademarks of The MathWorks, Inc and are used with permission The MathWorks does not warrant the accuracy of the text or exercises in this book This book’s use or discussion of MATLAB® and Simulink® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® and Simulink® software CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2012 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20110823 International Standard Book Number-13: 978-1-4398-1203-7 (eBook - PDF); 978-1-4398-1202-0 (hbk.) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com © 2012 by Taylor & Francis Group, LLC Contents About the Series xi Preface xiii Authors xv List of Abbreviations Introductory concepts 1.1 Stochastic and deterministic signals, concepts of stationarity and ergodicity 1.2 Discrete signals 1.2.1 The sampling theorem 1.2.1.1 Aliasing 1.2.2 Quantization error 1.3 Linear time invariant systems 1.4 Duality of time and frequency domain 1.4.1 Continuous periodic signal 1.4.2 Infinite continuous signal 1.4.3 Finite discrete signal 1.4.4 Basic properties of Fourier transform 1.4.5 Power spectrum: the Plancherel theorem and Parseval’s theorem 1.4.6 Z-transform 1.4.7 Uncertainty principle 1.5 Hypotheses testing 1.5.1 The null and alternative hypothesis 1.5.2 Types of tests 1.5.3 Multiple comparison problem 1.5.3.1 Correcting the significance level 1.5.3.2 Parametric and nonparametric statistical maps 1.5.3.3 False discovery rate 1.6 Surrogate data techniques Single channel (univariate) signal 2.1 Filters 2.1.1 Designing filters xvii 1 4 5 10 10 11 11 12 13 14 15 15 16 17 18 19 20 20 23 23 25 v © 2012 by Taylor & Francis Group, LLC Practical Biomedical Signal Analysis Using MATLAB R vi 2.2 2.3 2.4 2.1.2 Changing the sampling frequency 27 2.1.3 Matched filters 28 2.1.4 Wiener filter 29 Probabilistic models 30 2.2.1 Hidden Markov model 30 2.2.2 Kalman filters 31 Stationary signals 33 2.3.1 Analytic tools in the time domain 33 2.3.1.1 Mean value, amplitude distributions 33 2.3.1.2 Entropy and information measure 34 2.3.1.3 Autocorrelation function 34 2.3.2 Analytic tools in the frequency domain 35 2.3.2.1 Estimators of spectral power density based on Fourier transform 35 2.3.2.1.1 Choice of windowing function 36 2.3.2.1.2 Errors of Fourier spectral estimate 37 2.3.2.1.3 Relation of spectral density and the autocorrelation function 39 2.3.2.1.4 Bispectrum and bicoherence 39 2.3.2.2 Parametric models: AR, ARMA 40 2.3.2.2.1 AR model parameter estimation 41 2.3.2.2.2 Choice of the AR model order 42 2.3.2.2.3 AR model power spectrum 42 2.3.2.2.4 Parametric description of the rhythms by AR model, FAD method 45 Non-stationary signals 47 2.4.1 Instantaneous amplitude and instantaneous frequency 47 2.4.2 Analytic tools in the time-frequency domain 48 2.4.2.1 Time-frequency energy distributions 48 2.4.2.1.1 Wigner-Ville distribution 49 2.4.2.1.2 Cohen class 50 2.4.2.2 Time-frequency signal decompositions 52 2.4.2.2.1 Short time Fourier transform and spectrogram 52 2.4.2.2.2 Continuous wavelet transform and scalogram 54 2.4.2.2.3 Discrete wavelet transform 56 2.4.2.2.4 Dyadic wavelet transform—multiresolution signal decomposition 56 2.4.2.2.5 Wavelet packets 59 2.4.2.2.6 Wavelets in MATLAB 60 2.4.2.2.7 Matching pursuit—MP 60 2.4.2.2.8 Comparison of time-frequency methods 63 2.4.2.2.9 Empirical mode decomposition and HilbertHuang transform 65 © 2012 by Taylor & Francis Group, LLC Contents 2.5 vii Non-linear methods of signal analysis 2.5.1 Lyapunov exponent 2.5.2 Correlation dimension 2.5.3 Detrended fluctuation analysis 2.5.4 Recurrence plots 2.5.5 Poincar´e map 2.5.6 Approximate and sample entropy 2.5.7 Limitations of non-linear methods 66 67 68 69 70 72 72 73 Multiple channels (multivariate) signals 3.1 Cross-estimators: cross-correlation, cross-spectra, coherence (ordinary, partial, multiple) 3.2 Multivariate autoregressive model (MVAR) 3.2.1 Formulation of MVAR model 3.2.2 MVAR in the frequency domain 3.3 Measures of directedness 3.3.1 Estimators based on the phase difference 3.3.2 Causality measures 3.3.2.1 Granger causality 3.3.2.2 Granger causality index 3.3.2.3 Directed transfer function 3.3.2.3.1 dDTF 3.3.2.3.2 SDTF 3.3.2.4 Partial directed coherence 3.4 Non-linear estimators of dependencies between signals 3.4.1 Non-linear correlation 3.4.2 Kullback-Leibler entropy, mutual information and transfer entropy 3.4.3 Generalized synchronization 3.4.4 Phase synchronization 3.4.5 Testing the reliability of the estimators of directedness 3.5 Comparison of the multichannel estimators of coupling between time series 3.6 Multivariate signal decompositions 3.6.1 Principal component analysis (PCA) 3.6.1.1 Definition 3.6.1.2 Computation 3.6.1.3 Possible applications 3.6.2 Independent components analysis (ICA) 3.6.2.1 Definition 3.6.2.2 Estimation 3.6.2.3 Computation 3.6.2.4 Possible applications 3.6.3 Multivariate matching pursuit (MMP) 75 © 2012 by Taylor & Francis Group, LLC 75 77 77 79 80 80 81 81 82 82 84 85 85 87 87 87 89 89 90 91 95 95 95 96 96 97 97 98 98 99 99 Practical Biomedical Signal Analysis Using MATLAB R viii Application to biomedical signals 4.1 Brain signals: local field potentials (LFP), electrocorticogram (ECoG), electroencephalogram (EEG), and magnetoencephalogram (MEG), event-related responses (ERP), and evoked fields (EF) 4.1.1 Generation of brain signals 4.1.2 EEG/MEG rhythms 4.1.3 EEG measurement, electrode systems 4.1.4 MEG measurement, sensor systems 4.1.5 Elimination of artifacts 4.1.6 Analysis of continuous EEG signals 4.1.6.1 Single channel analysis 4.1.6.2 Multiple channel analysis 4.1.6.2.1 Mapping 4.1.6.2.2 Measuring of dependence between EEG signals 4.1.6.3 Sleep EEG analysis 4.1.6.4 Analysis of EEG in epilepsy 4.1.6.4.1 Quantification of seizures 4.1.6.4.2 Seizure detection and prediction 4.1.6.4.3 Localization of an epileptic focus 4.1.6.5 EEG in monitoring and anesthesia 4.1.6.5.1 Monitoring brain injury by quantitative EEG 4.1.6.5.2 Monitoring of EEG during anesthesia 4.1.7 Analysis of epoched EEG signals 4.1.7.1 Analysis of phase locked responses 4.1.7.1.1 Time averaging 4.1.7.1.2 Influence of noise correlation 4.1.7.1.3 Variations in latency 4.1.7.1.4 Habituation 4.1.7.2 In pursuit of single trial evoked responses 4.1.7.2.1 Wiener filters 4.1.7.2.2 Model based approach 4.1.7.2.3 Time-frequency parametric methods 4.1.7.2.4 ERP topography 4.1.7.3 Analysis of non-phase locked responses 4.1.7.3.1 Event-related synchronization and desynchronization 4.1.7.3.2 Classical frequency band methods 4.1.7.3.3 Time-frequency methods 4.1.7.3.4 ERD/ERS in the study of iEEG 4.1.7.3.5 Event-related time-varying functional connectivity 4.1.7.3.6 Functional connectivity estimation from intracranial electrical activity © 2012 by Taylor & Francis Group, LLC 101 101 103 105 107 109 109 115 116 117 117 118 122 129 130 133 137 138 138 138 139 141 141 143 143 144 145 145 145 146 147 150 150 151 153 156 158 163 Contents 4.2 4.3 4.4 4.5 ix 4.1.7.3.7 Statistical assessment of time-varying connectivity 4.1.8 Multimodal integration of EEG and fMRI signals Heart signals 4.2.1 Electrocardiogram 4.2.1.1 Measurement standards 4.2.1.2 Physiological background and clinical applications 4.2.1.3 Processing of ECG 4.2.1.3.1 Artifact removal 4.2.1.3.2 Morphological ECG features 4.2.1.3.3 Spatial representation of ECG activity; body surface potential mapping and vectorcardiography 4.2.1.3.4 Statistical methods and models for ECG analysis 4.2.1.3.5 ECG patterns classification 4.2.2 Heart rate variability 4.2.2.1 Time-domain methods of HRV analysis 4.2.2.2 Frequency-domain methods of HRV analysis 4.2.2.3 Relation of HRV to other signals 4.2.2.4 Non-linear methods of HRV analysis 4.2.2.4.1 Empirical mode decomposition 4.2.2.4.2 Entropy measures 4.2.2.4.3 Detrended fluctuation analysis 4.2.2.4.4 Poincar´e and recurrence plots 4.2.2.4.5 Effectiveness of non-linear methods 4.2.3 Fetal ECG 4.2.4 Magnetocardiogram and fetal magnetocardiogram 4.2.4.1 Magnetocardiogram 4.2.4.2 Fetal MCG Electromyogram 4.3.1 Measurement techniques and physiological background 4.3.2 Quantification of EMG features 4.3.3 Decomposition of needle EMG 4.3.4 Surface EMG 4.3.4.1 Surface EMG decomposition Gastro-intestinal signals Acoustic signals 4.5.1 Phonocardiogram 4.5.2 Otoacoustic emissions 166 167 169 169 169 170 173 173 175 176 178 179 180 180 181 183 184 185 186 187 188 189 190 195 195 199 200 201 205 206 210 211 218 221 221 224 References 231 Index 291 © 2012 by Taylor & Francis Group, LLC ... (1.13) Practical Biomedical Signal Analysis Using MATLAB R 1.2 Discrete signals In nature, most of the signals of interest are some physical values changing in time or space The biomedical signals... 89 89 90 91 95 95 95 96 96 97 97 98 98 99 99 Practical Biomedical Signal Analysis Using MATLAB R viii Application to biomedical signals 4.1 Brain signals: local field potentials (LFP), electrocorticogram.. .Practical Biomedical Signal Analysis Using MATLAB © 2012 by Taylor & Francis Group, LLC Series in Medical Physics and Biomedical Engineering Series Editors: