Two-Dimensional Digital Filters

WU-SHENG Lu is Professor in the Department of Electrical and Computer Engineering, Univer¬sity of Victoria, British Columbia, Canada. He is a senior member of the Institute of Electrical and Electronics Engineers and is the author of two books and numerous book chapters and journal articles. Dr. Lu received the B.S. degree (1964) in mathematics from Fudan University, Shanghai, People's Republic of China, the M.E. degree (1981) in automation from the East China Normal University, Shanghai, and the M.S. degree (1983) in electrical engineering and the Ph.D. degree (1984) in control science, both from the University of Minnesota, Minneapolis. ANDREAS ANTONIOU is Professor in the Department of Electrical and Computer Engineering, University of Victoria, British Columbia, Canada. The author of one book and numerous papers and book chapters, he is a Fellow of the Institute of Electrical and Electronics Engineers and the Institution of Electrical Engineers and a member of the Association of Professional Engineers and Geoscientists of British Columbia and the Canadian Society for Electrical and Computer Engineer-ing. Dr. Antoniou received the B.Sc. (1963) and the Ph.D. (1966) degrees in electrical engineering from the University of London, England.

• Preface -- Introduction -- Fundamentals -- 1.1 Introduction -- 1.2 2-D Discrete Signals -- 1.3 The 2-D Digital Filter as a System -- 1.4 Characterization -- 1.5 Representation in Terms of Flow Graphs and Networks -- 1.6 Introduction to Space-Domain Analysis -- 1.7 Stability -- 1.8 Realization -- 1.9 Multiple-Input—Multiple-Output Filters -- 1.10 Multidimensional Filters -- Reference -- Problems -- 2 State-Space Methods -- 2.1 Introduction -- 2.2 The Givone—Roesser Model -- 2.3 Space—Domain Analysis -- 2.4 Controllability and Observability -- 2.5 Realization -- References -- Problems -- 3 Transform Methods -- 3.1 Introduction -- 3.2 The 2-D z Transform -- 3.3 The 2-D Fourier Transform -- 3.4 The Sampling Process -- References -- Problems -- 4 The Application of the z Transform -- 4.1 Introduction -- 4.2 The Transfer Function -- 4.3 Stability -- 4.4 Space-Domain Analysis -- 4.5 Frequency-Domain Analysis -- References -- Problems -- 5 Stability Analysis -- 5.1 Introduction -- 5.2 Stability Analysis in Frequency Domain -- 5.3 Stability Analysis in State-Space Domain -- 5.4 2-D Lyapunov Stability Theory -- 5.5 Stability of Low-Order Filters -- References -- Problems -- 6 Approximations for Nonrecursive Filters -- 6.1 Introduction -- 6.2 Properties of 2-D Nonrecursive Filters -- 6.3 Design Based on Fourier Series -- 6.4 Design Based on Transformations -- References -- Problems -- 7 Approximations for Recursive Filters -- 7.1 Introduction -- 7.2 Transformations -- 7.3 Method of Hirano and Aggarwal -- 7.4 Design of Circularly Symmetric Filters -- 7.5 Constantinides Transformations -- 7.6 Design of Filters Satisfying Prescribed Specifications -- References -- Problems -- 8 Design of Recursive Filters by Optimization -- 8.1 Introduction -- 8.2 Design by Least pth Optimization -- 8.3 Minimax Method -- 8.4 Design Based on Two-Variable Network Theory -- 8.5 Design of Recursive Filters Using Singular-Value -- Decomposition -- References -- Problems -- 9 Design of Nonrecursive Filters by Optimization -- 9.1 Introduction -- 9.2 Minimax Design of Linear-Phase Nonrecursive Filters -- 9.3 Design of Linear-Phase Nonrecursive Filters Using SVD -- References -- Problems -- 10 Realization -- 10.1 Introduction -- 10.2 Nonrecursive Realizations Based on the McClellan -- Transformation -- 10.3 Nonrecursive Realizations Based on Matrix -- Decompositions -- 10.4 Direct Realization of Recursive Filters -- 10.5 LUD Realization of Recursive Filters -- 10.6 Indirect Realization of Recursive Filters -- References -- Problems -- 11 Finite Wordlength Effects -- 11.1 Introduction -- 11.2 Quantization Errors and Their Computation -- 11.3 State-Space Structures with Minimized Roundoff Noise -- 11.4 Limit Cycles -- References -- Problems -- 12 Implementation -- 12.1 Introduction -- 12.2 2-D Discrete Fourier Transform -- 12.3 Computation of 2-D DFT -- 12.4 Systolic Implementation -- References -- Problems -- 13 Applications -- 13.1 Introduction -- 13.2 Applications of Linear 2-D Filters to Image -- Enhancement -- 13.3 Image Restoration -- 13.4 Applications of Linear 2-D Fan Filters to Seismic. Signal -- Processing -- References -- Problems -- Index.