Signal Processing for Neuroscientists

Dedication

Preface

Chapter 1: Introduction

1.1 OVERVIEW

1.2 BIOMEDICAL SIGNALS

1.3 BIOPOTENTIALS

1.4 EXAMPLES OF BIOMEDICAL SIGNALS

1.5 ANALOG-TO-DIGITAL CONVERSION

1.6 MOVING SIGNALS INTO THE MATLAB ANALYSIS ENVIRONMENT

APPENDIX 1.1

Chapter 2: Data Acquisition

2.1 RATIONALE

2.2 THE MEASUREMENT CHAIN

2.3 SAMPLING AND NYQUIST FREQUENCY IN THE FREQUENCY DOMAIN

2.4 THE MOVE TO THE DIGITAL DOMAIN

Appendix 2.1

Chapter 3: Noise

3.1 INTRODUCTION

3.2 NOISE STATISTICS

3.3 SIGNAL-TO-NOISE RATIO

3.4 NOISE SOURCES

APPENDIX 3.1

APPENDIX 3.2

APPENDIX 3.3

APPENDIX 3.4

Chapter 4: Signal Averaging

4.1 INTRODUCTION

4.2 TIME LOCKED SIGNALS

4.3 SIGNAL AVERAGING AND RANDOM NOISE

4.4 NOISE ESTIMATES AND THE ± AVERAGE

4.5 SIGNAL AVERAGING AND NONRANDOM NOISE

4.6 NOISE AS A FRIEND OF THE SIGNAL AVERAGER

4.7 EVOKED POTENTIALS

4.8 OVERVIEW OF COMMONLY APPLIED TIME DOMAIN ANALYSIS TECHNIQUES

Chapter 5: Real and Complex Fourier Series

5.1 INTRODUCTION

5.2 THE FOURIER SERIES

5.3 THE COMPLEX FOURIER SERIES

5.4 EXAMPLES

APPENDIX 5.1

APPENDIX 5.2

Chapter 6: Continuous, Discrete, and Fast Fourier Transform

6.1 INTRODUCTION

6.2 THE FOURIER TRANSFORM

6.3 DISCRETE FOURIER TRANSFORM AND THE FFT ALGORITHM

6.4 UNEVENLY SAMPLED DATA

Chapter 7: Fourier Transform Applications

7.1 SPECTRAL ANALYSIS

7.2 TOMOGRAPHY

APPENDIX 7.1

Chapter 8: LTI Systems, Convolution, Correlation, and Coherence

8.1 INTRODUCTION

8.2 LINEAR TIME INVARIANT (LTI) SYSTEM

8.3 CONVOLUTION

8.4 AUTOCORRELATION AND CROSS-CORRELATION

8.5 COHERENCE

APPENDIX 8.1

Chapter 9: Laplace and z-Transform

9.1 INTRODUCTION

9.2 THE USE OF TRANSFORMS TO SOLVE ODEs

9.3 THE LAPLACE TRANSFORM

9.4 EXAMPLES OF THE LAPLACE TRANSFORM

9.5 THE Z-TRANSFORM

9.6 THE Z-TRANSFORM AND ITS INVERSE

9.7 EXAMPLE OF THE z-TRANSFORM

APPENDIX 9.1

APPENDIX 9.2

APPENDIX 9.3

Chapter 10: Introduction to Filters: The RC Circuit

10.1 INTRODUCTION

10.2 FILTER TYPES AND THEIR FREQUENCY DOMAIN CHARACTERISTICS

10.3 RECIPE FOR AN EXPERIMENT WITH AN RC CIRCUIT

Chapter 11: Filters: Analysis

11.1 INTRODUCTION

11.2 THE RC CIRCUIT

11.3 THE EXPERIMENTAL DATA

APPENDIX 11.1

APPENDIX 11.2

APPENDIX 11.3

Chapter 12: Filters: Specification, Bode Plot, and Nyquist Plot

12.1 INTRODUCTION: FILTERS AS LINEAR TIME INVARIANT (LTI) SYSTEMS

12.2 TIME DOMAIN RESPONSE

12.3 THE FREQUENCY CHARACTERISTIC

12.4 NOISE AND THE FILTER FREQUENCY RESPONSE

Chapter 13: Filters: Digital Filters

13.1 INTRODUCTION

13.2 IIR AND FIR DIGITAL FILTERS

13.3 AR, MA, AND ARMA FILTERS

13.4 FREQUENCY CHARACTERISTIC OF DIGITAL FILTERS

13.5 MATLAB IMPLEMENTATION

13.6 FILTER TYPES

13.7 FILTER BANK

13.8 FILTERS IN THE SPATIAL DOMAIN

APPENDIX 13.1

Chapter 14: Spike Train Analysis

14.1 INTRODUCTION

14.2 POISSON PROCESSES AND POISSON DISTRIBUTIONS

14.3 ENTROPY AND INFORMATION

14.4 THE AUTOCORRELATION FUNCTION

14.5 CROSS-CORRELATION

APPENDIX 14.1

APPENDIX 14.2

Chapter 15: Wavelet Analysis: Time Domain Properties

15.1 INTRODUCTION

15.2 WAVELET TRANSFORM

15.3 OTHER WAVELET FUNCTIONS

15.4 TWO-DIMENSIONAL APPLICATION

APPENDIX 15.1

Chapter 16: Wavelet Analysis: Frequency Domain Properties

16.1 INTRODUCTION

16.2 THE CONTINUOUS WAVELET TRANSFORM (CWT)

16.3 TIME FREQUENCY RESOLUTION

16.4 MATLAB WAVELET EXAMPLES

Chapter 17: Nonlinear Techniques

17.1 INTRODUCTION

17.2 NONLINEAR DETERMINISTIC PROCESSES

17.3 LINEAR TECHNIQUES FAIL TO DESCRIBE NONLINEAR DYNAMICS

17.4 EMBEDDING

17.5 METRICS FOR CHARACTERIZING NONLINEAR PROCESSES

17.6 APPLICATION TO BRAIN ELECTRICAL ACTIVITY

References

Index