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E-grāmata: Nonlinear Digital Filtering with Python: An Introduction

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(GeoVera Holdings, Inc., CA, USA), (Tampere University of Technology, Finland)
  • Formāts: 300 pages
  • Izdošanas datums: 03-Sep-2018
  • Izdevniecība: CRC Press Inc
  • Valoda: eng
  • ISBN-13: 9781498714136
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Nonlinear Digital Filtering with Python: An IntroductionPalielināt
  • Formāts: 300 pages
  • Izdošanas datums: 03-Sep-2018
  • Izdevniecība: CRC Press Inc
  • Valoda: eng
  • ISBN-13: 9781498714136
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Nonlinear Digital Filtering with Python: An Introduction discusses important structural filter classes including the median filter and a number of its extensions (e.g., weighted and recursive median filters), and Volterra filters based on polynomial nonlinearities. Adopting both structural and behavioral approaches in characterizing and designing nonlinear digital filters, this book:Begins with an expedient introduction to programming in the free, open-source computing environment of PythonUses results from algebra and the theory of functional equations to construct and characterize behaviorally defined nonlinear filter classesAnalyzes the impact of a range of useful interconnection strategies on filter behavior, providing Python implementations of the presented filters and interconnection strategiesProposes practical, bottom-up strategies for designing more complex and capable filters from simpler components in a way that preserves the key properties of these componentsIllustrates the behavioral consequences of allowing recursive (i.e., feedback) interconnections in nonlinear digital filters while highlighting a challenging but promising research frontierNonlinear Digital Filtering with Python: An Introduction supplies essential knowledge useful for developing and implementing data cleaning filters for dynamic data analysis and time-series modeling.

Recenzijas

"The authors bring the reader from the consolidated world of linear filters into the variegate universe of nonlinear filters, and show how the main subclasses of digital nonlinear filters can be described on the basis of their structural and/or behavioral characteristics. This approach is complemented by the use of a free, open-source computing environmentPythonfor the implementation of the nonlinear digital filters presented in each chapter." Giovanni L. Sicuranza, University of Trieste, Italy

Preface ix
Authors xiii
1 Introduction
1(26)
1.1 Linear versus nonlinear filters: an example
2(8)
1.2 Why nonlinearity? Data cleaning filters
10(4)
1.3 The many forms of nonlinearity
14(5)
1.3.1 A simple nonlinear filter taxonomy
15(2)
1.3.2 Recursive filters: instability and chaos
17(2)
1.4 Python and reproducible research
19(6)
1.4.1 A very brief introduction to Python
20(1)
1.4.2 Reproducible research
21(3)
1.4.3 How this book was developed
24(1)
1.5 Organization of this book
25(2)
2 Python
27(50)
2.1 A high-level overview of the language
27(6)
2.1.1 How Python programs work
28(1)
2.1.2 Using Python interactively
28(4)
2.1.3 Using Python from the command prompt
32(1)
2.2 Key language elements
33(25)
2.2.1 The general structure of Python
34(1)
2.2.2 Object types
35(2)
2.2.3 Data types
37(2)
2.2.4 Lists: a key data type
39(2)
2.2.5 Tuples: immutable lists
41(1)
2.2.6 Character strings
42(3)
2.2.7 Dictionaries: another key data type
45(2)
2.2.8 Functions
47(2)
2.2.9 Control structures
49(4)
2.2.10 Input and output
53(5)
2.3 Caveat emptor: a few Python quirks
58(4)
2.3.1 In-place operations, side-effects, and None returns
58(1)
2.3.2 Deep versus shallow copies
59(2)
2.3.3 Default values for function parameters
61(1)
2.4 A few filtering examples
62(9)
2.4.1 The SymmetricFilter function
62(2)
2.4.2 Moving window end effects and the Extend function
64(2)
2.4.3 The SMfilter function
66(3)
2.4.4 The LinearFIRfilter function
69(2)
2.5 Learning more about Python
71(6)
3 Linear and Volterra Filters
77(28)
3.1 Linear digital filters
78(8)
3.1.1 Linear filter representations
78(4)
3.1.2 Ideal filters and idempotence
82(2)
3.1.3 Positive-linear filters
84(2)
3.2 Linearity, smoothness, and harmonics
86(7)
3.3 Volterra filters
93(9)
3.3.1 The Volterra filter structure
94(1)
3.3.2 Some important special cases
94(7)
3.3.3 General block-oriented structures
101(1)
3.4 Universal approximations
102(3)
3.4.1 Specific results
102(2)
3.4.2 Limitations of universal approximation
104(1)
4 Median Filters and Some Extensions
105(44)
4.1 The standard median filter
105(8)
4.1.1 The problem of edge jitter
106(3)
4.1.2 Median filter root sequences
109(4)
4.2 Median filter cascades
113(3)
4.2.1 Median filter convergence
113(1)
4.2.2 The data sieve
114(2)
4.3 Order statistic filters
116(1)
4.4 The recursive median filter
117(2)
4.4.1 Definition of the recursive median filter
117(1)
4.4.2 Root sequences and idempotence
118(1)
4.4.3 A simple example
119(1)
4.5 Weighted median filters
119(15)
4.5.1 Weighted medians
121(3)
4.5.2 The weighted median filter
124(4)
4.5.3 A weighted median filter example
128(1)
4.5.4 Weighted median filter root sequences
129(1)
4.5.5 Center-weighted median filters
130(1)
4.5.6 Recursive weighted median filters
131(2)
4.5.7 Weighted median filter cascades
133(1)
4.6 Threshold decompositions and stack filters
134(3)
4.7 The Hampel filter
137(5)
4.7.1 Decision-theoretic filters
137(2)
4.7.2 Relation to the median filter
139(1)
4.7.3 MADM implosion: a cautionary note
139(1)
4.7.4 A Hampel filter example
140(2)
4.8 Python implementations
142(6)
4.9
Chapter summary
148(1)
5 Forms of Nonlinear Behavior
149(20)
5.1 Linearity versus additivity
150(2)
5.2 Homogeneity and positive homogeneity
152(5)
5.2.1 Homogeneity
152(2)
5.2.2 Positive homogeneity
154(2)
5.2.3 L-filters
156(1)
5.3 Generalized homogeneity
157(6)
5.3.1 Homogeneity of order zero
159(2)
5.3.2 Ranks are positive homogeneous of order zero
161(1)
5.3.3 Generalized combination filters
162(1)
5.4 Location-invariance
163(3)
5.4.1 The Gastwirth filter
164(1)
5.4.2 Mallows' class of nonlinear smoothers
165(1)
5.5 Restricted linearity
166(2)
5.6 Nonlinear structure versus behavior
168(1)
6 Composite Structures: Bottom-up Design
169(52)
6.1 A practical overview
169(4)
6.1.1 Cascades, categories, and LULU filters
169(1)
6.1.2 Parallel combinations, groups, and MMD filters
170(2)
6.1.3 Algebraic clones and the FMH filter
172(1)
6.2 Cascade interconnections and categories
173(16)
6.2.1 A brief introduction to category theory
173(3)
6.2.2 Filter categories
176(9)
6.2.3 The LULU filter category
185(4)
6.3 Parallel interconnections and groupoids
189(7)
6.3.1 Two illustrative examples
189(1)
6.3.2 Groups, monoids, semigroups, and groupoids
190(2)
6.3.3 Parallel combinations of K-linear filters
192(2)
6.3.4 Associative binary operators
194(1)
6.3.5 Positive homogeneous associative binary operators
195(1)
6.4 Clones: more general interconnections
196(8)
6.4.1 Basic concepts of clones
196(2)
6.4.2 General filter clone characteristics
198(1)
6.4.3 Clone representation of the Hampel filter
199(1)
6.4.4 The L-filter clone
200(4)
6.5 Python implementations
204(15)
6.6 Extensions to more general settings
219(2)
7 Recursive Structures and Stability
221(52)
7.1 What is different about recursive filters?
222(2)
7.2 Recursive filter classes
224(2)
7.3 Initializing recursive filters
226(2)
7.4 BIBO stability
228(4)
7.4.1 The concept of BIBO stability
228(1)
7.4.2 BIBO stability of non-recursive filters
229(1)
7.4.3 A rational filter counterexample
230(1)
7.4.4 BIBO stability of recursive filters
230(1)
7.4.5 Finite stability
231(1)
7.5 Steady-state responses
232(4)
7.5.1 Steady-state characterizations
232(2)
7.5.2 Consequences of ouput multiplicity
234(2)
7.6 Asymptotic stability
236(11)
7.6.1 General formulation of the problem
236(2)
7.6.2 Asymptotic stability of linear recursive filters
238(4)
7.6.3 Asymptotic and BIBO stability are different
242(3)
7.6.4 Input-dependent stability
245(1)
7.6.5 PAC for nonrecursive filters
246(1)
7.7 Inherently nonlinear behavior
247(4)
7.7.1 Subharmonic generation
248(2)
7.7.2 Chaos
250(1)
7.8 Fading memory filters
251(2)
7.9 Structured Lipschitz filters
253(4)
7.9.1 Basic definitions
254(1)
7.9.2 Stability results
255(1)
7.9.3 Examples of structured Lipschitz filters
256(1)
7.10 Behavior of key nonlinear filter classes
257(8)
7.10.1 Linear recursive filters
257(1)
7.10.2 NFIR filters
258(1)
7.10.3 The recursive median filter
259(1)
7.10.4 Block-oriented filters
260(1)
7.10.5 Lur'e filters
261(1)
7.10.6 Bilinear filters
262(1)
7.10.7 Output-affine filters
263(2)
7.10.8 Polynomial recursive filters
265(1)
7.11 Stability of interconnected systems
265(5)
7.12 Challenges and potential of recursive filters
270(3)
7.12.1 Block-oriented designs
271(1)
7.12.2 Output affine filters
271(1)
7.12.3 ZPSL filters
272(1)
Bibliography 273(10)
Index 283
Ronald K. Pearson is a data scientist with DataRobot. He previously held industrial, business, and academic positions at organizations including the DuPont Company, Swiss Federal Institute of Technology (ETH Zurich), Tampere University of Technology, and Travelers Companies. He holds a Ph.D in electrical engineering and computer science from the Massachusetts Institute of Technology, and has published conference and journal papers on topics ranging from nonlinear dynamic model structure selection to the problems of disguised missing data in predictive modeling. Dr. Pearson has authored or co-authored four previous books, the most recent being Exploring Data in Engineering, the Sciences, and Medicine.

Moncef Gabbouj is an Academy of Finland professor of signal processing at Tampere University of Technology. He holds a B.Sc in electrical engineering from Oklahoma State University, and an M.Sc and Ph.D in electrical engineering from Purdue University. Dr. Gabbouj is internationally recognized for his research in nonlinear signal and image processing and analysis. His research also includes multimedia analysis, indexing and retrieval, machine learning, voice conversion, and video processing and coding. Previously, Dr. Gabbouj held visiting professorships at institutions including the Hong Kong University of Science and Technology, Purdue University, University of Southern California, and American University of Sharjah.
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