Least square estimation with applications to digital signal processing:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Wiley
1985
|
| Schriftenreihe: | A Wiley-Interscience publication
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIII, 412 S. |
| ISBN: | 047187857X |
Internformat
MARC
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| 245 | 1 | 0 | |a Least square estimation with applications to digital signal processing |c Arthur A. Giordano ; Frank M. Hsu |
| 264 | 1 | |a New York u.a. |b Wiley |c 1985 | |
| 300 | |a XXIII, 412 S. | ||
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| 650 | 4 | |a Estimation theory |x Data processing | |
| 650 | 4 | |a Least squares |x Data processing | |
| 650 | 4 | |a Signal processing |x Digital techniques | |
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Datensatz im Suchindex
| _version_ | 1804114781676765184 |
|---|---|
| adam_text | Contents
NOTATION xvii
1 INTRODUCTION 1
1.1 Basis of Least Square Theory 2
1.2 Summary of Least Square Algorithms and Associated
Applications 3
1.3 Estimation by Least Squares and other Methods 7
1.3.1 MAP Estimation, 9
1.3.2 ML Estimation, 9
Part 1 Mathematical Formulations of the Least Square
Error Algorithms
2 INTRODUCTION TO LEAST SQUARES THEORY IS
2.1 Classical Least Squares 15
2.1.1 Derivation of Fourier Series Coefficients by
Differentiation, 16
2.1.2 Derivation of Fourier Series Coefficients by
Orthogonality Principle, 18
2.1.3 Evaluation of the Minimum Average Square
Error, 18
2.1.4 Orthogonal Function Expansions, 19
2.2 Least Squares Optimization in Hilbert Space 20
2.2.1 Hilbert Space Definition, 20
2.2.2 Generalized Orthogonal Function Expansion, 24
xi
xii CONTENTS
2.3 Orthogonality Principle in Hilbert Space 25
2.3.1 Geometric Interpretation of Orthogonality
Principle, 25
2.3.2 Gram Schmidt Orthogonalization Procedure, 27
2.3.3 Formal Theory of Optimization in Hilbert
Space, 28
3 LEAST SQUARE ESTIMATION ALGORITHMS—PART I 40
3.1 Durbin Algorithm 40
3.1.1 Model Description, 40
3.1.2 Derivation of Yule Walker Equations by
Differentiation, 42
3.1.3 Derivation of Yule Walker Equations by
Orthogonality Principle, 43
3.1.4 Durbin Recursive Solution, 44
3.2 Levinson Algorithm 49
3.2.1 Model Description, 49
3.2.2 Derivation of Normal Equations by
Differentiation, 49
3.2.3 Derivation of Normal Equations by the
Orthogonality Principle, 50
3.2.4 Levinson Recursive Solution, 51
3.3 Cholesky Decomposition Algorithm 58
3.4 Autocorrelation Coefficients Computational Methods 63
3.5 Forward and Backward Prediction 66
3.5.1 Model Description, 66
3.5.2 Lattice Structure with Known Autocorrelation
Coefficients, 69
3.5.3 Burg Algorithm, 70
4 LEAST SQUARE ESTIMATION ALGORITHMS—PART II 80
4.1 Recursive Least Squares Lattice Algorithms 80
4.1.1 Model Description, 80
4.1.2 Order Update for Coefficients, 84
4.1.3 Order Update for Minimum Mean Square
Error, 90
4.1.4 Error Updates, 91
4.1.5 Time Update, 93
CONTENTS Xiii
4.1.6 Summary of Recursive Least Squares Lattice
Algorithm, 93
4.1.7 Lattice Structure Development, 95
4.1.8 Specialization of Lattice Structure to Burg
Algorithm, 98
Appendix Derivation of the Time Update Recursion 102
5 LEAST SQUARE ESTIMATION ALGORITHMS—PART III 109
5.1 Simple Least Squares Estimation 109
5.2 Minimum Variance Weighted Least Squares
(Gauss Markov) 111
5.3 Minimum Variance Least Squares (Kalman) 114
5.3.1 Kalman Recursive Estimation Algorithm, 117
5.3.2 Derivation of Kalman Recursive Estimation
Algorithm Using the Loss Function, 120
5.4 Square Root Kalman Algorithm 126
5.4.1 U D Factorization, 126
5.4.2 Mathematical Development of U D Kalman
Algorithm, 126
5.4.3 Summary of U D Kalman Algorithm, 135
Part 2 Application of Least Square Analysis to Digital Signal
Processing
6 EQUALIZATION 139
6.1 Discrete Model of a Continuous Time Communication
System 139
6.2 Wireline and Radio Channels 143
6.3 Equalization Techniques 147
6.3.1 Linear Equalization Using Transversal Filters, 148
6.3.2 Decision Feedback Equalization, 150
6.3.3 Adaptive Equalization Techniques, 152
6.3.3.1 Steepest Descent Method, 153
6.3.3.2 Lattice Structure Method for Linear
Equalization, 154
6.3.3.3 Gradient Lattice Structure for Linear
Equalization, 162
XIV CONTENTS
6.3.3.4 Lattice Structure for Decision Feedback
Equalization, 164
6.3.3.5 Kalman Method, 170
6.4 Equalizer Performance Examples 174
6.4.1 Linear Equalizer Performance Examples, 175
6.4.1.1 Telephone Channel Example, 175
6.4.1.2 Multipath Radio Channel Example, 184
6.4.2 Decision Feedback Equalizer Performance
Examples, 198
6.4.2.1 Troposcatter Channel Example, 198
6.4.2.2 HF Channel Example, 207
6.4.3 Performance of Lattice Structures, 223
Appendix Derivation of Recursive Equations Needed in Gradient
Lattice Structure for Linear Equalization 229
7 POWER SPECTRAL ESTIMATION 238
7.1 Historical Overview 238
7.2 Traditional Power Spectral Estimation Technique 239
7.2.1 Power Spectrum Estimation Using Periodgram
Methods, 244
7.3 Autoregressive Method 250
7.3.1 AR Technique, 250
7.3.2 Durbin Method, 253
7.3.3 Selection of the Order of the Prediction Filter, 254
8 DIGITAL WHITENING IN SPREAD SPECTRUM (SS)
COMMUNICATIONS 266
8.1 Introduction 266
8.2 Overview of Spread Spectrum Communications 266
8.3 Augmentation of PN Spread Spectrum Communications
with Digital Whitening 268
8.4 SS Communication System Model with Digital
Whitening 269
8.5 Digital Whitening Algorithms 272
8.6 Decision Variable for Digitally Whitened SS Communication
System 275
8.6.1 Moments of the PN Correlator Output without
Digital Whitening, 275
CONTENTS XV
8.6.2 Moments of the PN Correlator Output with Digital
Whitening, 277
8.6.3 SNR Improvement Factor, 278
8.6.4 Bit Error Rate Computations, 279
8.7 Digital Whitening Performance Results 280
8.8 Performance Bound for SNR Improvement Factor 286
9 ADAPTIVE ARRAYS 292
9.1 Adaptive Array Techniques 292
9.2 General Configurations of Adaptive Arrays 293
9.3 Spatial Adaptive Signal Processing Techniques 295
9.4 Adaptive Array Experimental Results of Riegler and
Compton 296
9.5 Mathematical Model for the Transmitted and Received
Signals in Spread Spectrum Array Processing Applications 303
9.6 Adaptive Antenna Interference Cancellers 306
9.7 Baseband Antenna Array Combining Techniques 313
9.7.1 Minimum Mean Square Error (MSE) Diversity
Antenna Combining Technique with Independent
Gaussian Noise, 314
9.7.2 Minimum Mean Square Error (MSE) Diversity
Antenna Combining Technique with Colored
Gaussian Noise, 316
9.8 Error Rate Performance 319
9.9 Minimum MSE Algorithms 326
9.10 Computer Simulation for Speed of Convergence with
Minimum MSE Algorithms 330
Appendix Minimum Mean Square Error (MSE) Diversity
Antenna Combining Technique with Jointly Stationary Gaussian
Noise Processes 332
10 DUAL CHANNEL INTERFERENCE MITIGATION 335
10.1 Dual Channel Digital Signal Transmission Model 336
10.2 Reduction of Interchannel Interference by the MSE
Algorithm 336
10.3 Performance Results 338
Appendix Derivation of Weights for Interchannel
Interference Mitigation 341
XVI CONTENTS
11 LEAST SQUARES TECHNIQUES IN DIGITAL
SPEECH PROCESSING 343
11.1 Introduction 343
11.2 Speech Production Model and Speech Characteristics 344
11.3 Speech Coding Techniques 346
11.4 Linear Prediction of Speech 347
11.4.1 Speech Analysis, 350
11.4.1.1 Estimation of Predictor Coefficients by
Covariance Method, 351
11.4.1.2 Estimation of Prediction Coefficients by
Correlation Method, 352
11.4.1.3 Stability Considerations in the Correlation
Method, 353
11.4.1.4 Pitch Estimation, 355
11.4.1.5 Voiced/Unvoiced Switch Estimation, 356
11.4.1.6 Gain Computation, 356
11.4.2 Speech Synthesis, 356
11.5 Time Domain Waveform Coding of Speech Signals 358
11.5.1 Pulse Code Modulation (PCM), 358
11.5.2 Differential Pulse Code Modulation (DPCM), 362
11.5.3 Delta Modulation, 372
11.5.4 Adaptive Predictive Coding (APC), 376
11.5.5 Comparison of Speech Encoding Techniques, 382
11.5.6 Additional Linear Prediction Algorithms, 383
11.6 Image Processing 383
APPENDIX: PRINCIPAL MATHEMATICAL RESULTS 386
INDEX 405
|
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| indexdate | 2024-07-09T15:12:11Z |
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| language | English |
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| spelling | Giordano, Arthur A. Verfasser aut Least square estimation with applications to digital signal processing Arthur A. Giordano ; Frank M. Hsu New York u.a. Wiley 1985 XXIII, 412 S. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Datenverarbeitung Estimation theory Data processing Least squares Data processing Signal processing Digital techniques Methode der kleinsten Quadrate (DE-588)4038974-1 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Digitale Signalverarbeitung (DE-588)4113314-6 gnd rswk-swf Methode der kleinsten Quadrate (DE-588)4038974-1 s Datenverarbeitung (DE-588)4011152-0 s DE-604 Digitale Signalverarbeitung (DE-588)4113314-6 s Hsu, Frank M. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000194465&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Giordano, Arthur A. Hsu, Frank M. Least square estimation with applications to digital signal processing Datenverarbeitung Estimation theory Data processing Least squares Data processing Signal processing Digital techniques Methode der kleinsten Quadrate (DE-588)4038974-1 gnd Datenverarbeitung (DE-588)4011152-0 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd |
| subject_GND | (DE-588)4038974-1 (DE-588)4011152-0 (DE-588)4113314-6 |
| title | Least square estimation with applications to digital signal processing |
| title_auth | Least square estimation with applications to digital signal processing |
| title_exact_search | Least square estimation with applications to digital signal processing |
| title_full | Least square estimation with applications to digital signal processing Arthur A. Giordano ; Frank M. Hsu |
| title_fullStr | Least square estimation with applications to digital signal processing Arthur A. Giordano ; Frank M. Hsu |
| title_full_unstemmed | Least square estimation with applications to digital signal processing Arthur A. Giordano ; Frank M. Hsu |
| title_short | Least square estimation with applications to digital signal processing |
| title_sort | least square estimation with applications to digital signal processing |
| topic | Datenverarbeitung Estimation theory Data processing Least squares Data processing Signal processing Digital techniques Methode der kleinsten Quadrate (DE-588)4038974-1 gnd Datenverarbeitung (DE-588)4011152-0 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd |
| topic_facet | Datenverarbeitung Estimation theory Data processing Least squares Data processing Signal processing Digital techniques Methode der kleinsten Quadrate Digitale Signalverarbeitung |
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