Author(s): Wim van Drongelen
Edition: 1
Publisher: Elsevier
Year: 2010
Language: English
Commentary: no TOC, cover
Pages: 179
Tags: Медицинские дисциплины;Неврология и нейрохирургия;
Front matter......Page 2
Copyright......Page 3
Preface......Page 4
Unevenly Sampled Data......Page 6
Lomb’s Algorithm......Page 8
A MATLAB Example......Page 12
The Hilbert Transform......Page 13
The Hilbert Transform in the Frequency Domain......Page 15
The Hilbert Transform in the Time Domain......Page 19
Examples......Page 20
Appendix 1.1......Page 22
Appendix 1.2......Page 23
Appendix 1.3......Page 24
Different Types of Models......Page 25
Examples of Parametric and Nonparametric Models......Page 27
Describing Discrete Time Data Sets......Page 30
Maclaurin Series......Page 32
Taylor Series......Page 34
Nonlinear Systems with Memory......Page 36
Taylor Series for a 2D Function......Page 40
Introduction......Page 42
Volterra Series......Page 45
Combined Input to a Second-Order Volterra System......Page 46
A Second-Order Volterra System......Page 48
Discrete Time Implementation......Page 52
Determining the Second-Order Kernel......Page 54
Determining the First-Order Kernel......Page 55
The LN Cascade......Page 56
The NL Cascade......Page 57
The LNL Cascade......Page 58
Sinusoidal Signals......Page 60
Introduction......Page 64
Wiener Kernels......Page 65
Derivation of the Second-Order Wiener Operator......Page 68
Orthogonality Between H0 and g2......Page 69
Orthogonality Between H1 and g2......Page 70
Determination of the Zero-Order Wiener Kernel......Page 72
Determination of the First-Order Wiener Kernel......Page 73
1D Example......Page 163
Implementation of the Cross-Correlation Method......Page 76
Relation between Wiener and Volterra Kernels......Page 80
Analyzing Spiking Neurons Stimulated with Noise......Page 82
Nonwhite Gaussian Input......Page 87
Summary......Page 89
Averages of Gaussian Random Variables......Page 90
Delay System as Volterra Operator......Page 92
Systems with Impulse Train Input......Page 94
Product Averages for the Poisson Impulse Train......Page 95
Orthogonal Terms of the Poisson–Wiener Series......Page 100
The First-Order Poisson–Wiener Operator......Page 101
The Second-Order Poisson–Wiener Operator......Page 102
Determination of the First-Order Poisson–Wiener Kernel......Page 106
Determination of the Second-Order Poisson–Wiener Kernel......Page 108
An Example of ICA Applied to EEG Signals......Page 155
Spiking Output......Page 114
Summary......Page 115
Expectation and Time Averages of Variables Following a Poisson Process......Page 116
Creating Impulse Trains Following a Poisson Process......Page 120
Introduction......Page 122
Mixing and Unmixing of Signals......Page 123
Principal Component Analysis......Page 126
Finding Principal Components......Page 129
A MATLAB Example......Page 131
Singular Value Decomposition......Page 134
Using PCA as a Filter......Page 136
Independent Component Analysis......Page 137
Entropy of Sources and Mixtures......Page 138
Using the Scalar Product to Find Independent Components......Page 144
A MATLAB Example......Page 146
What If Sources Are Not Uniformly Distributed?......Page 148
Can We Apply Smarter Approaches Than the Brute Force Technique?......Page 154
Eigenvalues and Eigenvectors......Page 158
Introduction......Page 161
Directed Transfer Function......Page 162
Multidimensional Example......Page 165
Implementation......Page 168
Examples......Page 170
Combination of Multichannel Methods......Page 177
References......Page 178
