Statistical spectral analysis: a nonprobabilistic theory
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, NJ
Prentice Hall
1988
|
| Edition: | 1. print. |
| Series: | Prentice Hall information and system sciences series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVI, 566 S. Ill. |
| ISBN: | 0138445729 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804115251310886912 |
|---|---|
| adam_text | CONTENTS
FOREWORD xiii
PREFACE xvii
ACKNOWLEDGMENTS xxi
GLOSSARIES xxiii
Part I Constant Phenomena 1
1 INTRODUCTION TO SPECTRAL ANALYSIS 3
A Objectives and Motives, 3
B Orientation, 5
/ What Is Spectral Analysis?, 5
2 Why Analyze Waveforms Into Sine Wave Components?, 7
C Origins of Spectral Analysis, 12
D Spectral Analysis and Periodicity, 20
E Summary, 21
F Overview of Part I, 22
Exercises, 23
Appendix 1-1: Linear Time-Invariant Transformations
and Fourier Transforms: A Review, 26
2 NONSTATISTICAL SPECTRAL ANALYSIS 34
A Temporal and Spectral Resolution, 35
B Data Tapering, 38
C Time-frequency Uncertainty Principle, 42
D Periodogram-Correlogram Relation, 42
E Finite-Average Autocorrelation and Pseudo Spectrum, 43
F Periodogram and Correlogram Relations for Filters, 46
G Local Average Power Spectral Density, 48
H Time Sampling and Aliasing, 49
1 Summary, 51
Exercises, 53
Appendix 2-1: Instantaneous Frequency, 63
vii
67
3 STATISTICAL SPECTRAL ANALYSIS
A Motivating Example, 68
B Temporal- and Spectral-Smoothing Equivalence, 72
C The Limit Spectrum, 74
D Examples of Spectral Density, 77
1 White Noise, 77
2 Sine Wave with Additive Noise, 78
3 Sine Wave with Multiplicative Noise (Amplitude Modulation), 78
4 Pulse-Amplitude Modulation, 79
5 Sine Wave with Amplitude and Phase Modulation, 80
E Time-Sampling and Aliasing, 81
F Time-Series Models, 83
1 The Moving Average Model, 84
2 The Autoregressive Model, 84
3 The ARMA Model, 85
G Statistical Inference, 85
H Summary, 87
Exercises, 88
Appendix 3-1: Band-pass Time-Series, 98
Appendix 3-2: Random-Signal Detection, 104
4 ANALOG METHODS 108
A Temporal and Spectral Smoothing, 109
B Fourier Transformation of Tapered Autocorrelation, 112
C Spectral Leakage and Prewhitening, 113
D Hopped Temporal Smoothing, 116
E Wave Analysis, 118
1 Complex Implementation, 118
2 Real Implementation, 120
F Demodulation, 120
1 Complex Implementation, 121
2 Real Implementation, 122
3 Swept-Frequency Implementation, 123
G A General Representation, 125
H Summary, 126
Exercises, 128
Appendix 4-1: Other Wave-Analysis Methods, 136
1 The Fano Identity, 136
2 The Schroeder-Atal Identity, 136
5 FRACTION-OF-TIME PROBABILISTIC ANALYSIS 138
A Motivation, 138
B Fraction-of-Time Probabilistic Model, 140
C Bias and Variability, 143
1 The Finite-Time Complex Spectrum, 144
2 The Finite-Time Spectrum, 145
3 Statistical Spectra, 147
4 Time-Frequency Uncertainty Condition, 159
D Resolution, Leakage, and Reliability: Design Trade-offs, 161
vill
Contents
E Summary, 169
Exercises, 170
6 DIGITAL METHODS
A Introduction, 179
B The DFT, 180
/ Resolution and Zero-Padding, 180
2 Circular Convolution, 185
3 The FST and CFT, 187
C Methods Based on the DFT, 192
1 Bartlett-Welch Method, 193
2 Wiener-Daniell Method, 195
3 Blackman-Tukey Method, 196
4 Channelizer Methods, 197
5 Minimum-Leakage Method, 198
D Fraction-of-time Probabilistic Analysis, 201
E Summary, 202
Exercises, 202
7 CROSS-SPECTRAL ANALYSIS
A Elements of Cross-Spectral Analysis, 211
B Coherence, 215
C Autocoherence and Periodicity, 220
D Measurement Methods, 223
1 Temporal and Spectral Smoothing, 224
2 Fourier Transformation of Tapered Cross Correlation, 224
3 Cross-Wave Analysis, 224
4 Cross Demodulation, 227
E Resolution, Leakage, and Reliability, 229
1 Cross periodogram, 229
2 Statistical Cross Spectra, 230
F Summary, 234
Exercises, 234
Appendix 7-1: Propagation-Path Identification, 239
Appendix 7-2: Distant-Source Detection, 240
Appendix 7-3: Time- and Frequency-Difference-of-Arrival Estimation, 241
8 TIME-VARIANT SPECTRAL ANALYSIS
A General Variation, 244
1 The Physical Spectrum, 244
2 Linear Time-Variant Systems, 246
3 Local Ergodicity, 249
B Periodic Variation, 250
C Summary, 251
Exercises, 252
9 PARAMETRIC METHODS
A Introduction, 254
B Autoregressive Modeling Theory, 255
Contents
179
211
244
254
ix
Part II
10
1 Yule-Walker Equations, 256
2 Levinson-Durbin Algorithm, 257
3 Linear Prediction, 258
4 Wold-Cramer Decomposition, 259
5 Maximum-Entropy Model, 261
6 Lattice Filter, 263
7 Cholesky Factorization and Correlation Matrix Inversion, 265
C Autoregressive Methods, 266
1 In troduction, 266
2 Least Squares Procedures, 273
3 Model-Order Determination, 281
4 Singular-Value Decomposition, 283
5 Maximum Likelihood Approach, 287
6 Discussion, 288
D ARMA Methods, 290
1 Modified Yule-Walker Equations, 291
2 Estimation of the AR Parameters, 292
3 Estimation of the MA Parameters, 293
E Experimental Study, 298
1 Periodogram Methods, 301
2 Minimum-Leakage Method, 306
3 Yule-Walker, Burg, and Forward-Backward Least-Squares AR
Methods, 306
4 Overdetermined-Normal-Equations AR Method, 307
5 Singular-Value-Decomposition Method, 318
6 Hybrid Method, 319
F Summary, 328
Exercises, 329
Appendix 9-1: Table of Data, 343
Periodic Phenomena
INTRODUCTION TO SECOND-ORDER PERIODICITY
A Motivation and Overview, 355
B Derivation of Fundamental Statistical Parameters 359
1 Generation of Spectral Lines from Second-Order Periodicity 359
2 Synchronized Averaging, 362
3 Cross-Spectral Analysis, 365
4 Optimum Generation of Spectral Lines, 367
C Relationships to Woodward Radar Ambiguity and Wigner-Ville
Distribution, 369
D Sine Waves and Principal Components 373
1 Linear Periodically Time-Variant Transformations, 373
2 Cyclostationary Stochastic Processes, 375
E The Link Between Deterministic and Probabilistic Theories, 376
F Multiple Periodicities, 378
G Summary, 380
Exercises, 381
351
355
x
Contents
384
11 CYCLIC SPECTRAL ANALYSIS
A Cyclic Periodogram and Cyclic Correlogram, 384
B Temporal and Spectral Smoothing, Resolution, and Reliability, 386
C The Limit Cyclic Spectrum, 389
1 Derivation, 389
2 Spectrum Types and Bandwidths, 390
3 Symmetries and Parseval Relations, 393
4 Cyclic Cross Spectra, 396
5 Spectral Autocoherence, 396
6 Filtering and Product Modulation, 398
D Linear Periodically Time-Variant Transformations, 405
1 General Input-Output Relations, 405
2 Rice s Representation, 409
E Summary, 414
Exercises, 414
12 EXAMPLES OF CYCLIC SPECTRA 419
A Pulse and Carrier Amplitude Modulation, 420
B Quadrature-Carrier Amplitude Modulation, 425
C Phase and Frequency Carrier Modulation, 428
D Digital Pulse Modulation, 434
E Digital Carrier Modulation, 442
1 Amplitude-Shift Keying, 442
2 Phase-Shift Keying, 443
3 Frequency-Shift Keying, 448
F Spread-Spectrum Modulation, 453
1 Direct Sequence PSK, 453
2 Frequency-Hopped FSK, 454
G Summary, 457
Exercises, 457
13 MEASUREMENT METHODS 463
A Temporal and Spectral Smoothing, 463
B Fourier Transformation of Tapered Cyclic Autocorrelation or Ambiguity
Function, 467
C Fourier Transformation of Spectrally Smoothed Wigner-Ville
Distribution, 470
D Cyclic Wave Analysis, 470
E Cyclic Demodulation, 475
F Summary, 477
Exercises, 478
14 APPLICATIONS 481
A Optimum Cyclic Filtering, 482
B Adaptive Cyclic Filtering, 485
C Cyclic System Identification, 488
D Cyclic Parameter Estimation and Synchronization, 493
E Cyclic Detection, 497
F Cyclic Array Processing, 503
Contents
xi
G Summary, 505
Exercises, 506
15 CYCLIC FRACTION-OF-TIME PROBABILISTIC ANALYSIS
A Cyclic Fraction-of-Time Probabilistic Model, 511
1 Cyclic Fraction-of-Time Distributions, 511
2 Cyclic Temporal Expectation, 517
3 Gaussian Almost Cyclostationary Time-Series, 521
B Probabilistic Analysis of Cyclic Spectrum Measurements, 525
/ A General Representation, 526
2 Resolution and Leakage, 527
3 Variability, 528
C Summary, 534
Exercises, 535
REFERENCES FOR PART I
REFERENCES FOR PART II
AUTHOR INDEX
SUBJECT INDEX
510
538
548
553
557
xii
|
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| spelling | Gardner, William A. Verfasser aut Statistical spectral analysis a nonprobabilistic theory 1. print. Englewood Cliffs, NJ Prentice Hall 1988 XXVI, 566 S. Ill. txt rdacontent n rdamedia nc rdacarrier Prentice Hall information and system sciences series Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Spektralanalyse Stochastik (DE-588)4056125-2 gnd rswk-swf Spektralanalyse Stochastik (DE-588)4056125-2 s DE-604 Zeitreihenanalyse (DE-588)4067486-1 s Spektraltheorie (DE-588)4116561-5 s 1\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000501170&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gardner, William A. Statistical spectral analysis a nonprobabilistic theory Zeitreihenanalyse (DE-588)4067486-1 gnd Spektraltheorie (DE-588)4116561-5 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4116561-5 (DE-588)4056125-2 |
| title | Statistical spectral analysis a nonprobabilistic theory |
| title_auth | Statistical spectral analysis a nonprobabilistic theory |
| title_exact_search | Statistical spectral analysis a nonprobabilistic theory |
| title_full | Statistical spectral analysis a nonprobabilistic theory |
| title_fullStr | Statistical spectral analysis a nonprobabilistic theory |
| title_full_unstemmed | Statistical spectral analysis a nonprobabilistic theory |
| title_short | Statistical spectral analysis |
| title_sort | statistical spectral analysis a nonprobabilistic theory |
| title_sub | a nonprobabilistic theory |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Spektraltheorie (DE-588)4116561-5 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd |
| topic_facet | Zeitreihenanalyse Spektraltheorie Spektralanalyse Stochastik |
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