Signal Processing for Neuroscientists (eBook)

Front cover 1
Signal Processing for Neuroscientists 4
Copyright page 5
Preface 8
Table of contents 10
Chapter 1: Introduction 12
1.1 OVERVIEW 12
1.2 BIOMEDICAL SIGNALS 13
1.3 BIOPOTENTIALS 13
1.4 EXAMPLES OF BIOMEDICAL SIGNALS 13
1.5 ANALOG-TO-DIGITAL CONVERSION 17
1.6 MOVING SIGNALS INTO THE MATLAB ANALYSIS ENVIRONMENT 18
APPENDIX 1.1 22
Chapter 2: Data Acquisition 26
2.1 RATIONALE 26
2.2 THE MEASUREMENT CHAIN 26
2.3 SAMPLING AND NYQUIST FREQUENCY IN THE FREQUENCY DOMAIN 37
2.4 THE MOVE TO THE DIGITAL DOMAIN 40
APPENDIX 2.1 41
Chapter 3: Noise 46
3.1 INTRODUCTION 46
3.2 NOISE STATISTICS 48
3.3 SIGNAL-TO-NOISE RATIO 52
3.4 NOISE SOURCES 54
APPENDIX 3.1 59
APPENDIX 3.2 60
APPENDIX 3.3 62
APPENDIX 3.4 63
Chapter 4: Signal Averaging 66
4.1 INTRODUCTION 66
4.2 TIME LOCKED SIGNALS 66
4.3 SIGNAL AVERAGING AND RANDOM NOISE 68
4.4 NOISE ESTIMATES AND THE ± AVERAGE 72
4.5 SIGNAL AVERAGING AND NONRANDOM NOISE 72
4.6 NOISE AS A FRIEND OF THE SIGNAL AVERAGER 74
4.7 EVOKED POTENTIALS 77
4.8 OVERVIEW OF COMMONLY APPLIED TIME DOMAIN ANALYSIS TECHNIQUES 79
Chapter 5: Real and Complex Fourier Series 82
5.1 INTRODUCTION 82
5.2 THE FOURIER SERIES 84
5.3 THE COMPLEX FOURIER SERIES 92
5.4 EXAMPLES 95
APPENDIX 5.1 98
APPENDIX 5.2 101
Chapter 6: Continuous, Discrete, and Fast Fourier Transform 102
6.1 INTRODUCTION 102
6.2 THE FOURIER TRANSFORM 102
6.3 DISCRETE FOURIER TRANSFORM AND THE FFT ALGORITHM 108
6.4 UNEVENLY SAMPLED DATA 116
Chapter 7: Fourier Transform Applications 118
7.1 SPECTRAL ANALYSIS 118
7.2 TOMOGRAPHY 128
APPENDIX 7.1 135
Chapter 8: LTI Systems, Convolution, Correlation, and Coherence 138
8.1 INTRODUCTION 138
8.2 LINEAR TIME INVARIANT (LTI) SYSTEM 138
8.3 CONVOLUTION 141
8.4 AUTOCORRELATION AND CROSS-CORRELATION 147
8.5 COHERENCE 153
APPENDIX 8.1 160
Chapter 9: Laplace and z-Transform 162
9.1 INTRODUCTION 162
9.2 THE USE OF TRANSFORMS TO SOLVE ODEs 162
9.3 THE LAPLACE TRANSFORM 164
9.4 EXAMPLES OF THE LAPLACE TRANSFORM 165
9.5 THE Z-TRANSFORM 170
9.6 THE Z-TRANSFORM AND ITS INVERSE 172
9.7 EXAMPLE OF THE z-TRANSFORM 173
APPENDIX 9.1 174
APPENDIX 9.2 175
APPENDIX 9.3 176
Chapter 10: Introduction to Filters: The RC Circuit 180
10.1 INTRODUCTION 180
10.2 FILTER TYPES AND THEIR FREQUENCY DOMAIN CHARACTERISTICS 180
10.3 RECIPE FOR AN EXPERIMENT WITH AN RC CIRCUIT 183
Chapter 11: Filters: Analysis 188
11.1 INTRODUCTION 188
11.2 THE RC CIRCUIT 188
11.3 THE EXPERIMENTAL DATA 194
APPENDIX 11.1 195
APPENDIX 11.2 197
APPENDIX 11.3 197
Chapter 12: Filters: Specification, Bode Plot, and Nyquist Plot 200
12.1 INTRODUCTION: FILTERS AS LINEAR TIME INVARIANT (LTI) SYSTEMS 200
12.2 TIME DOMAIN RESPONSE 201
12.3 THE FREQUENCY CHARACTERISTIC 204
12.4 NOISE AND THE FILTER FREQUENCY RESPONSE 211
Chapter 13: Filters: Digital Filters 216
13.1 INTRODUCTION 216
13.2 IIR AND FIR DIGITAL FILTERS 216
13.3 AR, MA, AND ARMA FILTERS 217
13.4 FREQUENCY CHARACTERISTIC OF DIGITAL FILTERS 218
13.5 MATLAB IMPLEMENTATION 220
13.6 FILTER TYPES 223
13.7 FILTER BANK 224
13.8 FILTERS IN THE SPATIAL DOMAIN 226
APPENDIX 13.1 227
Chapter 14: Spike Train Analysis 230
14.1 INTRODUCTION 230
14.2 POISSON PROCESSES AND POISSON DISTRIBUTIONS 234
14.3 ENTROPY AND INFORMATION 239
14.4 THE AUTOCORRELATION FUNCTION 245
14.5 CROSS-CORRELATION 250
APPENDIX 14.1 251
APPENDIX 14.2 253
Chapter 15: Wavelet Analysis: Time Domain Properties 256
15.1 INTRODUCTION 256
15.2 WAVELET TRANSFORM 256
15.3 OTHER WAVELET FUNCTIONS 268
15.4 TWO-DIMENSIONAL APPLICATION 271
APPENDIX 15.1 273
Chapter 16: Wavelet Analysis: Frequency Domain Properties 276
16.1 INTRODUCTION 276
16.2 THE CONTINUOUS WAVELET TRANSFORM (CWT) 276
16.3 TIME FREQUENCY RESOLUTION 280
16.4 MATLAB WAVELET EXAMPLES 286
Chapter 17: Nonlinear Techniques 290
17.1 INTRODUCTION 290
17.2 NONLINEAR DETERMINISTIC PROCESSES 291
17.3 LINEAR TECHNIQUES FAIL TO DESCRIBE NONLINEAR DYNAMICS 293
17.4 EMBEDDING 296
17.5 METRICS FOR CHARACTERIZING NONLINEAR PROCESSES 299
17.6 APPLICATION TO BRAIN ELECTRICAL ACTIVITY 305
References 308
Index 312