Two-Dimensional Digital Filters

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-Inputâ"Multiple-Output Filters -- 1.10 Multidimensional Filters -- Reference -- Problems -- 2 State-Space Methods -- 2.1 Introduction -- 2.2 The Givoneâ"Roesser Model -- 2.3 Spaceâ"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.