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E-raamat: Signal Processing for Neuroscientists

(Department of Pediatrics, University of Chicago, Chicago, IL, USA)
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  • Ilmumisaeg: 20-Apr-2018
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128104835
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Signal Processing for NeuroscientistsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 20-Apr-2018
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128104835
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Signal Processing for Neuroscientists, Second Edition provides an introduction to signal processing and modeling for those with a modest understanding of algebra, trigonometry and calculus. With a robust modeling component, this book describes modeling from the fundamental level of differential equations all the way up to practical applications in neuronal modeling. It features nine new chapters and an exercise section developed by the author. Since the modeling of systems and signal analysis are closely related, integrated presentation of these topics using identical or similar mathematics presents a didactic advantage and a significant resource for neuroscientists with quantitative interest.

Although each of the topics introduced could fill several volumes, this book provides a fundamental and uncluttered background for the non-specialist scientist or engineer to not only get applications started, but also evaluate more advanced literature on signal processing and modeling.

  • Includes an introduction to biomedical signals, noise characteristics, recording techniques, and the more advanced topics of linear, nonlinear and multi-channel systems analysis
  • Features new chapters on the fundamentals of modeling, application to neuronal modeling, Kalman filter, multi-taper power spectrum estimation, and practice exercises
  • Contains the basics and background for more advanced topics in extensive notes and appendices
  • Includes practical examples of algorithm development and implementation in MATLAB
  • Features a companion website with MATLAB scripts, data files, figures and video lectures
Preface to the Second Edition xv
Preface to the Companion Volume xvii
Preface to the First Edition xix
1 Introduction
1.1 Overview
1(1)
1.2 Biomedical Signals
2(1)
1.3 Biopotentials
2(1)
1.4 Examples of Biomedical Signals
3(4)
1.5 Analog-to-Digital Conversion
7(1)
1.6 Moving Signals Into the MATLAB® Analysis Environment
8(9)
Appendix 1.1
12(2)
Exercises
14(1)
References
15(2)
2 Data Acquisition
2.1 Rationale
17(1)
2.2 The Measurement Chain
18(10)
2.3 Sampling and Nyquist Frequency in the Frequency Domain
28(3)
2.4 The Move to the Digital Domain
31(6)
Appendix 2.1
32(3)
Exercises
35(1)
References
36(1)
3 Noise
3.1 Introduction
37(2)
3.2 Noise Statistics
39(4)
3.3 Signal-to-Noise Ratio
43(2)
3.4 Noise Sources
45(14)
Appendix 3.1
50(1)
Appendix 3.2
51(2)
Appendix 3.3
53(1)
Appendix 3.4
54(1)
Appendix 3.5 Laplace and Fourier Transforms of Probability Density Functions
54(2)
Exercises
56(1)
References
57(2)
4 Signal Averaging
4.1 Introduction
59(1)
4.2 Time-Locked Signals
59(3)
4.3 Signal Averaging and Random Noise
62(3)
4.4 Noise Estimates
65(2)
4.5 Signal Averaging and Nonrandom Noise
67(1)
4.6 Noise as a Friend of the Signal Averager
68(4)
4.7 Evoked Potentials
72(2)
4.8 Overview of Commonly Applied Time Domain Analysis Techniques
74(7)
Appendix 4.1 Expectation of the Product of Independent Random Variables
77(1)
Exercises
78(2)
References
80(1)
5 Real and Complex Fourier Series
5.1 Introduction
81(2)
5.2 The Fourier Series
83(8)
5.3 The Complex Fourier Series
91(12)
Examples
94(4)
Appendix 5.1
98(2)
Appendix 5.2
100(1)
Exercises
101(2)
6 Continuous, Discrete, and Fast Fourier Transform
6.1 Introduction
103(1)
6.2 The Fourier Transform
103(6)
6.3 Discrete Fourier Transform and the Fast Fourier Transform Algorithm
109(10)
Exercises
117(1)
Reference
118(1)
7 1-D and 2-D Fourier Transform Applications
7.1 Spectral Analysis
119(11)
7.2 Two-Dimensional Fourier Transform Applications in Imaging
130(23)
Appendix 7.1
148(3)
Exercises
151(1)
References
152(1)
8 Lomb's Algorithm and Multitaper Power Spectrum Estimation
8.1 Overview
153(1)
8.2 Unevenly Sampled Data
153(8)
8.3 Errors in the Periodogram
161(20)
Appendix 8.1
176(1)
Appendix 8.2
177(2)
Exercises
179(1)
References
179(2)
9 Differential Equations: Introduction
9.1 Modeling Dynamics
181(2)
9.2 How to Formulate an Ordinary Differential Equation
183(1)
9.3 Solving First- and Second-Order Ordinary Differential Equations
184(3)
9.4 Ordinary Differential Equations With a Forcing Term
187(4)
9.5 Representation of Higher-Order Ordinary Differential Equations as a Set of First-Order Ones
191(6)
9.6 Transforms to Solve Ordinary Differential Equations
197(2)
Exercises
197(1)
References
198(1)
10 Differential Equations: Phase Space and Numerical Solutions
10.1 Graphical Representation of Flow and Phase Space
199(4)
10.2 Numerical Solution of an ODE
203(5)
10.3 Partial Differential Equations
208(3)
Exercises
210(1)
Reference
210(1)
11 Modeling
11.1 Introduction
211(1)
11.2 Different Types of Models
211(2)
11.3 Examples of Parametric and Nonparametric Models
213(4)
11.4 Polynomials
217(7)
11.5 Nonlinear Systems With Memory
224(7)
Appendix 11.1
228(1)
Exercises
229(1)
References
229(2)
12 Laplace and z-Transform
12.1 Introduction
231(1)
12.2 The Use of Transforms to Solve Ordinary Differential Equations
231(2)
12.3 The Laplace Transform
233(2)
12.4 Examples of the Laplace Transform
235(4)
12.5 The z-Transform
239(3)
12.6 The z-Transform and Its Inverse
242(1)
12.7 Example of the z-Transform
243(8)
Appendix 12.1
244(1)
Appendix 12.2
244(2)
Appendix 12.3
246(3)
Exercises
249(1)
References
250(1)
13 LTI Systems: Convolution, Correlation, Coherence, and the Hilbert Transform
13.1 Introduction
251(1)
13.2 Linear Time-Invariant System
252(2)
13.3 Convolution
254(7)
13.4 Autocorrelation and Cross-Correlation
261(7)
13.5 Coherence
268(5)
13.6 The Hilbert Transform
273(16)
Appendix 13.1
283(2)
Appendix 13.2
285(1)
Appendix 13.3
286(1)
Exercises
286(2)
References
288(1)
14 Causality
14.1 Introduction
289(1)
14.2 Granger Causality
290(1)
14.3 Directed Transfer Function
291(11)
14.4 Applications of Causal Analysis
302(5)
Exercises
304(1)
References
305(2)
15 Introduction to Filters: The RC-Circuit
15.1 Introduction
307(1)
15.2 Filter Types and Their Frequency Domain Characteristics
308(2)
15.3 Recipe for an Experiment With an RC-Circuit
310(5)
Exercise
314(1)
References
314(1)
16 Filters: Analysis
16.1 Introduction
315(1)
16.2 The RC Circuit
316(6)
16.3 The Experimental Data
322(7)
Appendix 16.1
323(2)
Appendix 16.2
325(1)
Appendix 16.3
325(2)
Exercises
327(2)
17 Filters: Specification, Bode Plot, Nyquist Plot
17.1 Introduction: Filters as Linear Time-Invariant Systems
329(1)
17.2 Time Domain Response
330(4)
17.3 The Frequency Characteristic
334(6)
17.4 Noise and the Filter Frequency Response
340(5)
Exercises
343(2)
18 Filters: Digital Filters
18.1 Introduction
345(1)
18.2 Infinite Impulse Response and Finite Impulse Response Digital Filters
345(2)
18.3 Autoregressive, Moving Average, and ARMA Filters
347(1)
18.4 Frequency Characteristics of Digital Filters
347(2)
18.5 MATLAB® Implementation
349(4)
18.6 Filter Types
353(1)
18.7 Filter Bank
354(1)
18.8 Filters in the Spatial Domain
354(7)
Appendix 18.1
357(1)
Exercises
358(1)
Reference
359(2)
19 Kalman Filter
19.1 Introduction
361(1)
19.2 Introductory Terminology
362(4)
19.3 Derivation of a Kalman Filter for a Simple Case
366(4)
19.4 MATLAB® Example
370(2)
19.5 Use of the Kalman Filter to Estimate Model Parameters
372(3)
Appendix 19.1 Details of the Steps Between Eqs. (19.17) and (19.18)
372(2)
Exercises
374(1)
References
374(1)
20 Spike Train Analysis
20.1 Introduction
375(4)
20.2 Poisson Processes and Poisson Distributions
379(5)
20.3 Entropy and Information
384(5)
20.4 The Autocorrelation Function
389(6)
20.5 Cross-Correlation
395(6)
Appendix 20.1
397(1)
Appendix 20.2
398(1)
Exercises
399(1)
References
400(1)
21 Wavelet Analysis: Time Domain Properties
21.1 Introduction
401(1)
21.2 Wavelet Transform
401(13)
21.3 Other Wavelet Functions
414(4)
21.4 2-D Application
418(7)
Appendix 21.1
421(1)
Appendix 21.2
422(1)
Exercises
423(1)
References
423(2)
22 Wavelet Analysis: Frequency Domain Properties
22.1 Introduction
425(1)
22.2 The Continuous Wavelet Transform
426(4)
22.3 Time---Frequency Resolution
430(6)
22.4 MATLAB® Wavelet Examples
436(7)
Appendix 22.1
438(2)
Exercises
440(2)
Reference
442(1)
23 Low-Dimensional Nonlinear Dynamics: Fixed Points, Limit Cycles, and Bifurcations
23.1 Introduction
443(1)
23.2 Nonlinear Dynamics in Continuous and Discrete Time
444(4)
23.3 Effects of Parameter Selection on Linear and Nonlinear Systems
448(4)
23.4 Application to Modeling Neural Excitability
452(10)
23.5 Codimension-2 Bifurcations
462(5)
Appendix 23.1
462(3)
Exercises
465(1)
References
465(2)
24 Volterra Series
24.1 Introduction
467(3)
24.2 Volterra Series
470(4)
24.3 A Second-Order Volterra System
474(7)
24.4 General Second-Order System
481(1)
24.5 System Tests for Internal Structure
482(6)
24.6 Sinusoidal Signals
488(5)
Exercises
491(1)
References
492(1)
25 Wiener Series
25.1 Introduction
493(1)
25.2 Wiener Kernels
494(8)
25.3 Determination of the Zeroth-, First-, and Second-Order Wiener Kernels
502(5)
25.4 Implementation of the Cross-Correlation Method
507(5)
25.5 Relation Between Wiener and Volterra Kernels
512(1)
25.6 Analyzing Spiking Neurons Stimulated With Noise
513(6)
25.7 Nonwhite Gaussian Input
519(2)
25.8 Summary
521(8)
Appendix 25.1
523(2)
Appendix 25.2
525(1)
Exercises
526(1)
References
527(2)
26 Poisson---Wiener Series
26.1 Introduction
529(1)
26.2 Systems With Impulse Train Input
529(13)
26.3 Determination of the Zeroth-, First-, and Second-Order Poisson---Wiener Kernels
542(7)
26.4 Implementation of the Cross-Correlation Method
549(2)
26.5 Spiking Output
551(2)
26.6 Summary
553(8)
Appendix 26.1
553(5)
Appendix 26.2
558(2)
Exercises
560(1)
References
560(1)
27 Nonlinear Techniques
27.1 Introduction
561(1)
27.2 Nonlinear Deterministic Processes
562(2)
27.3 Linear Techniques Fail to Describe Nonlinear Dynamics
564(3)
27.4 Embedding
567(2)
27.5 Metrics for Characterizing Nonlinear Processes
569(7)
27.6 Application to Brain Electrical Activity
576(3)
Exercises
577(1)
References
577(2)
28 Decomposition of Multichannel Data
28.1 Introduction
579(2)
28.2 Mixing and Unmixing of Signals
581(3)
28.3 Principal Component Analysis
584(12)
28.4 Independent Component Analysis
596(23)
Exercises
616(1)
References
617(2)
29 Modeling Neural Systems: Cellular Models
29.1 Introduction
619(1)
29.2 The Hodgkin and Huxley Formalism
620(13)
29.3 Models That Can Be Derived From the Hodgkin and Huxley Formalism
633(14)
Appendix 29.1
640(2)
Appendix 29.2 Building the Integrate-and-Fire Circuit
642(2)
Exercises
644(1)
References
644(3)
30 Modeling Neural Systems: Network Models
30.1 Introduction
647(2)
30.2 Networks of Individual Cell Models
649(8)
30.3 Mean Field Network Models
657(18)
30.4 Spatiotemporal Model for the Electroencephalogram
675(3)
30.5 A Field Equation for the Electroencephalogram
678(8)
30.6 Models With a Stochastic Component
686(8)
30.7 Concluding Remarks
694(13)
Appendix 30.1 Linearization of the Wilson---Cowan Equations
696(2)
Appendix 30.2 Adjusting Weights by Backpropagation of the Error
698(3)
Exercises
701(1)
References
702(5)
Index 707
Wim van Drongelen studied Biophysics at the University Leiden, The Netherlands. After a period in the Laboratoire d'Electrophysiologie, Université Claude Bernard, Lyon, France, he received the Doctoral degree cum laude. In 1980 he received the Ph.D. degree. He worked for the Netherlands Organization for the Advancement of Pure Research (ZWO) in the Department of Animal Physiology, Wageningen, The Netherlands. He lectured and founded a Medical Technology Department at the HBO Institute Twente, The Netherlands. In 1986 he joined the Benelux office of Nicolet Biomedical as an Application Specialist and in 1993 he relocated to Madison, WI, USA where he was involved in research and development of equipment for clinical neurophysiology and neuromonitoring. In 2001 he joined the Epilepsy Center at The University of Chicago, Chicago, IL, USA. Currently he is Professor of Pediatrics, Neurology, and Computational Neuroscience. In addition to his faculty position he serves as Technical and Research Director of the Pediatric Epilepsy Center and he is Senior Fellow with the Computation Institute. Since 2003 he teaches applied mathematics courses for the Committee on Computational Neuroscience. His ongoing research interests include the application of signal processing and modeling techniques to help resolve problems in neurophysiology and neuropathology. For details of recent work see http://epilepsylab.uchicago.edu/
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