Digital signal processing with Python programming
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| Format: | Buch |
| Sprache: | English |
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London
ISTE
2017
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| Schriftenreihe: | Digital signal and image processing series
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| Online-Zugang: | Inhaltsverzeichnis Klappentext |
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| 245 | 1 | 0 | |a Digital signal processing with Python programming |c Maurice Charbit |
| 264 | 1 | |a London |b ISTE |c 2017 | |
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Datensatz im Suchindex
| _version_ | 1819685711652061184 |
|---|---|
| adam_text | Contents
Preface..................................................................... ix
Notations and Abbreviations................................................. xi
A Few Functions of Python®................................................ xiii
Chapter 1. Useful Maths...................................................... 1
LI. Basic concepts on probability ....................................... 1
1.2. Conditional expectation............................................ 10
1.3. Projection theorem................................................. 11
1.3.1. Conditional expectation........................................ 14
1.4. Gaussianity........................................................ 14
1.4.1. Gaussian random variable ...................................... 14
1.4.2. Gaussian random vectors........................................ 15
1.4.3. Gaussian conditional distribution.............................. 16
1.5. Random variable transformation..................................... 18
1.5.1. General expression ............................................ 18
1.5.2. Law of the sum of two random variables...................... 19
1.5.3. 5-method....................................................... 20
1.6. Fundamental theorems of statistics ................................ 22
1.7. A few probability distributions.................................... 24
Chapter 2. Statistical Inferences .......................................... 29
2.1. First step: visualizing data....................................... 29
2.1.1. Scatter plot.................................................. 29
2.1.2. Histogram/boxplot.............................................. 30
2.1.3. Q-Q plot...................................................... 32
2.2. Reduction of dataset dimensionality................................ 34
vi Digitai Signal Processing with Python Programming
2.2. L PC A............................................................. 34
2.2.2. LDA.............................................................. 36
2.3. Some vocabulary...................................................... 40
2.3.1. Statistical inference............................................ 40
2.4. Statistical model.................................................... 41
2.4.1. Notation ........................................................ 42
2.5. Hypothesis testing................................................... 43
2.5.1. Simple hypotheses .............................................. 45
2.5.2. Generalized likelihood ratio test (GLRT)...................... 50
2.5.3. x2 goodness-of-fit test ......................................... 57
2.6. Statistical estimation .............................................. 58
2.6.1. General principles............................................... 58
2.6.2. Least squares method............................................. 62
2.6.3. Least squares method for the linear model..................... 64
2.6.4. Method of moments................................................ 81
2.6.5. Maximum likelihood approach...................................... 84
2.6.6. Logistic regression ......................................... . 100
2.6.7. Non-parametric estimation of probability distribution........... 103
2.6.8. Bootstrap and others............................................ 107
Chapter 3. Inferences on HMM................................................. 113
3.1. Hidden Markov models (HMM).......................................... 113
3.2. Inferences on HMM................................................... 116
3.3. Filtering: general case............................................. 117
3.4. Gaussian linear case: Kalman algorithm ............................. 118
3.4.1. Kalman filter................................................... 118
3.4.2. RTS smoother................................................... 127
3.5. Discrete finite Markov case......................................... 129
3.5.1. Forward-backward formulas....................................... 130
3.5.2. Smoothing formula at one instant................................ 133
3.5.3. Smoothing formula at two successive instants.................. 134
3.5.4. HMM learning using the EM algorithm........................... 135
3.5.5. The Viterbi algorithm........................................... 137
Chapter 4. Monte-Carlo Methods............................................... 141
4.1. Fundamental theorems................................................ 141
4.2. Stating the problem................................................. 141
4.3. Generating random variables......................................... 144
4.3.1. The cumulative function inversion method........................ 144
4.3.2. The variable transformation method.............................. 147
4.3.3. Acceptance-rejection method..................................... 149
4.3.4. Sequential methods.............................................. 151
4.4. Variance reduction.................................................. 156
Contents vii
4.4.1. Importance sampling........................................... 156
4.4.2. Stratification................................................ 160
4.4.3. Antithetic variates......................................... 164
Chapter 5. Hints and Solutions ............................................ 167
5.1. Useful maths...................................................... 167
5.2. Statistical inferences............................................ 170
5.3. Inferences on HMM................................................. 226
5.4. Monte-Carlo methods............................................... 251
Bibliography .............................................................. 261
Index
263
This book addresses the basic principles of statistical inference.
The first chapter recalls the basis of probabilities. The second
chapter is devoted to point estimation, the hypothesis test,
including p-values, the confidence region determination,
mentioning only the most important concepts. The main practical
approaches, such as the least squares minimization, the moment
method and the likelihood maximization, are broadly detailed.
The following chapter is devoted to hidden Markov models
(HMM) which are the basis of the more recent algorithms in signal
and image processing. The final chapter is devoted to Monte-
Carlo methods, which provide useful estimation tools using well-
chosen random generators.
To understand a theory well, it must be supported by practical
examples. Therefore, 16 computational examples and 62
computational exercises using a real dataset are proposed. The
solutions are coded in Python language and provides in an
appendix.
Maurice Charbit is Professor at Telecom ParisTech, France. He is a
teacher in probability theory, signal processing, communication
theory and statistics for data processing. With regard to research,
his main areas of interest are: (i) the Bayesian approach for
hidden Markov models, (ii) the 3D model-based approach for face
tracking, and (iii) processing for multiple sensor arrays with
applications to infrasonic systems.
www.iste.co.uk
Wiley
|
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| discipline | Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV044001521 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T05:38:43Z |
| institution | BVB |
| isbn | 9781786301260 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029409434 |
| oclc_num | 1002255080 |
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| owner_facet | DE-703 DE-706 DE-634 |
| physical | xvi, 267 Seiten Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | ISTE |
| record_format | marc |
| series2 | Digital signal and image processing series |
| spellingShingle | Charbit, Maurice Digital signal processing with Python programming Signalverarbeitung (DE-588)4054947-1 gnd Signalanalyse (DE-588)4181260-8 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Python Programmiersprache (DE-588)4434275-5 gnd |
| subject_GND | (DE-588)4054947-1 (DE-588)4181260-8 (DE-588)4113314-6 (DE-588)4434275-5 |
| title | Digital signal processing with Python programming |
| title_auth | Digital signal processing with Python programming |
| title_exact_search | Digital signal processing with Python programming |
| title_full | Digital signal processing with Python programming Maurice Charbit |
| title_fullStr | Digital signal processing with Python programming Maurice Charbit |
| title_full_unstemmed | Digital signal processing with Python programming Maurice Charbit |
| title_short | Digital signal processing with Python programming |
| title_sort | digital signal processing with python programming |
| topic | Signalverarbeitung (DE-588)4054947-1 gnd Signalanalyse (DE-588)4181260-8 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Python Programmiersprache (DE-588)4434275-5 gnd |
| topic_facet | Signalverarbeitung Signalanalyse Digitale Signalverarbeitung Python Programmiersprache |
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