Two-Dimensional Digital Filters

by Lu; Wu-Sheng

• ISBN13: 9780824784348
• ISBN10: 0824784340
• Format: Hardcover
• Copyright: 1992-07-15
• Publisher: CRC Press

Summary

Presents basic theories, techniques, and procedures used to analyze, design, and implement two-dimensional filters; and surveys a number of applications in image and seismic data processing that demonstrate their use in real-world signal processing. For graduate students in electrical and computer e

Table of Contents

Preface
Introduction	p. 1
Fundamentals
Introduction	p. 5
2-D Discrete Signals	p. 5
The 2-D Digital Filter as a System	p. 10
Characterization	p. 12
Representation in Terms of Flow Graphs and Networks	p. 14
Introduction to Space-Domain Analysis	p. 16
Stability	p. 27
Realization	p. 29
Multiple-Input-Multiple-Output Filters	p. 32
Multidimensional Filters	p. 34
Reference	p. 35
Problems	p. 35
State-Space Methods
Introduction	p. 38
The Givone-Roesser Model	p. 39
Space-Domain Analysis	p. 48
Controllability and Observability	p. 50
Realization	p. 52
References	p. 52
Problems	p. 53
Transform Methods
Introduction	p. 55
The 2-D z Transform	p. 56
The 2-D Fourier Transform	p. 65
The Sampling Process	p. 68
References	p. 74
Problems	p. 74
The Application of the z Transform
Introduction	p. 77
The Transfer Function	p. 77
Stability	p. 82
Space-Domain Analysis	p. 84
Frequency-Domain Analysis	p. 86
References	p. 103
Problems	p. 103
Stability Analysis
Introduction	p. 106
Stability Analysis in Frequency Domain	p. 107
Stability Analysis in State-Space Domain	p. 118
2-D Lyapunov Stability Theory	p. 121
Stability of Low-Order Filters	p. 124
References	p. 127
Problems	p. 129
Approximations for Nonrecursive Filters
Introduction	p. 132
Properties of 2-D Nonrecursive Filters	p. 133
Design Based on Fourier Series	p. 137
Design Based on Transformations	p. 163
References	p. 173
Problems	p. 174
Approximations for Recursive Filters
Introduction	p. 176
Transformations	p. 177
Method of Hirano and Aggarwal	p. 190
Design of Circularly Symmetric Filters	p. 204
Constantinides Transformations	p. 218
Design of Filters Satisfying Prescribed Specifications	p. 219
References	p. 226
Problems	p. 227
Design of Recursive Filters by Optimization
Introduction	p. 230
Design by Least pth Optimization	p. 231
Minimax Method	p. 236
Design Based on Two-Variable Network Theory	p. 244
Design of Recursive Filters Using Singular-Value Decomposition	p. 251
References	p. 263
Problems	p. 264
Design of Nonrecursive Filters by Optimization
Introduction	p. 266
Minimax Design of Linear-Phase Nonrecursive Filters	p. 267
Design of Linear-Phase Nonrecursive Filters Using SVD	p. 271
References	p. 282
Problems	p. 283
Realization
Introduction	p. 284
Nonrecursive Realizations Based on the McClellan Transformation	p. 285
Nonrecursive Realizations Based on Matrix Decompositions	p. 289
Direct Realization of Recursive Filters	p. 294
LUD Realization of Recursive Filters	p. 295
Indirect Realization of Recursive Filters	p. 300
References	p. 313
Problems	p. 315
Finite Wordlength Effects
Introduction	p. 317
Quantization Errors and Their Computation	p. 318
State-Space Structures with Minimized Roundoff Noise	p. 325
Limit Cycles	p. 334
References	p. 339
Problems	p. 340
Implementation
Introduction	p. 342
2-D Discrete Fourier Transform	p. 343
Computation of 2-D DFT	p. 347
Systolic Implementation	p. 350
References	p. 357
Problems	p. 358
Applications
Introduction	p. 360
Applications of Linear 2-D Filters to Image Enhancement	p. 360
Image Restoration	p. 370
Applications of Linear 2-D Fan Filters to Seismic Signal Processing	p. 379
References	p. 386
Problems	p. 387
Index	p. 388
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