Foreword
|
ix |
Preface
|
xi |
I Some Basic Notions |
1 |
Chapter 1 Signal: Going Digital |
3 |
1.1 Sampling |
4 |
1.2 Drawback: Aliasing |
5 |
1.3 Advantage: Checksums |
8 |
Chapter 2 Analysis |
11 |
2.1 Inner Product—A Measure of Fit |
15 |
2.2 Orthogonality |
15 |
2.3 Frequency and Phase |
16 |
Chapter 3 Spectrum |
19 |
3.1 Example Calculations |
21 |
3.2 Uncertainty Principle and Resolution |
25 |
3.3 Real-World Spectra |
26 |
Chapter 4 Between Time and Frequency |
29 |
4.1 Spectrogram |
29 |
4.2 Interpretation of the Spectrogram |
32 |
4.3 Wavelets |
33 |
4.4 Wigner Transform and Cross-Terms |
35 |
References |
38 |
Chapter 5
Choosing the Representation |
39 |
5.1 Gabor
Dictionary |
39 |
5.2 Adaptive
Approximation |
41 |
5.3 Matching
Pursuit |
43 |
5.4 Time-Frequency Energy Density |
44 |
References |
46 |
Chapter 6 Advantages of Adaptive Approximations |
47 |
6.1 Explicit Parameterization of Transients |
47 |
6.2 Automatic Negotiation of Time-Frequency Tradeoff |
50 |
6.3 Freedom from Arbitrary Settings |
52 |
6.4 A Unified Framework |
53 |
Chapter 7 Caveats and Practical Issues |
55 |
7.1 Dictionary Density |
55 |
7.2 Number of Waveforms in the Expansion |
57 |
7.3 Statistical Bias |
58 |
7.4 Limitations of Gabor Dictionaries |
59 |
References |
60 |
II EEG Analysis |
61 |
Chapter 8 Parameterization of EEG Transients |
63 |
8.1 Selecting Relevant Structures |
66 |
8.2 Sleep Spindles and Slow Waves |
68 |
8.3 Real-World Problems |
72 |
8.4 Hypnogram and Continuous Description of Sleep |
75 |
8.5 Sensitivity to Phase and Frequency |
77 |
8.6 Nonoscillating Structures |
79 |
8.7 Epileptic EEG Spikes |
82 |
References |
|
Chapter 9 Epileptic Seizures |
87 |
9.1 Series of Spikes |
88 |
9.2 Periodicity and Greedy Algorithms |
89 |
9.3 Evolution of Seizures |
|
9.4 Gabor Atom Density |
95 |
References |
99 |
Chapter 10 Event-Related Desynchronization and
Synchronization |
101 |
10.1 Conventional ERD/ERS Quantification |
102 |
10.2 A Complete Time-Frequency Picture |
104 |
10.3 ERD/ERS in the Time-Frequency Plane |
105 |
10.4 Other Estimates of Signal’s Energy
Density |
108 |
References |
112 |
Chapter 11 Selective Estimates of Energy |
115 |
11.1 ERD/ERS Enhancement |
117 |
11.2 Pharmaco EEG |
117 |
References |
129 |
Chapter 12 Spatial Localization of Cerebral Sources |
131 |
12.1 EEG Inverse Solutions |
132 |
12.2 Is It a Tomography? |
133 |
12.3 Selection of Structures for Localization |
134 |
12.4 Localization of Sleep Spindles |
137 |
References |
139 |
III Equations and Technical Details |
141 |
Chapter 13 Adaptive Approximations and Matching Pursuit
|
143 |
13.1 Notation |
143 |
13.2 Linear Expansions |
144 |
13.3 Time-Frequency Distributions |
145 |
13.4 Adaptive Time-Frequency Approximations |
146 |
13.5 Matching Pursuit Algorithm |
147 |
13.6 Orthogonalization |
148 |
13.7 Stopping Criteria |
149 |
13.8 Matching Pursuit with Gabor Dictionaries |
151 |
13.9 Statistical Bias |
153 |
13.10 MP-Based Estimate of Signal’s Energy
Density |
155 |
13.11 An Interesting Failure of the Greedy Algorithm |
157 |
13.12 Multichannel Matching Pursuit |
158 |
References |
163 |
Chapter 14 Implementation: Details and Tricks |
167 |
14.1 Optimal Phase of a Gabor Function |
168 |
14.2 Product Update Formula |
170 |
14.3 Sin, Cos, and Exp: Fast Calculations and Tables |
170 |
References |
172 |
Chapter 15 Statistical Significance of Changes in the
Time-Frequency Plane |
173 |
15.1 Reference Epoch |
173 |
15.2 Resolution Elements |
174 |
15.3 Statistics |
175 |
15.4 Resampling |
176 |
15.5 Parametric Tests |
177 |
15.6 Correction for Multiple Comparisons |
177 |
References |
179 |
About the Author |
181 |
Index |
183 |