ISBN: 3540641610
TITLE: Magnitude and Delay Approximation of 1-D and 2-D Digital Filters
AUTHOR: Shenoi, Belle A.
TOC:

1 Classical Methods of Approximation 1
1.1 Introduction 1
1.2 Classical Filter Theory 2
1.3 Types of Approximation 4
1.4 Butterworth Approximation 9
1.4.1 Example 1.1 14
1.4.2 Example 1.2 17
1.5 Chebyshev Approximation 18
1.5.1 Example 1.3 22
1.6 Inverse Chebyshev Approximation 23
1.6.1 Example 1.4 26
1.7 Elliptic Approximation 27
1.8 Least Squares Approximation 31
1.9 Analog Frequency Transformations 34
1.10 Highpass Filter 34
1.10.1 Example 1.5 35
1.11 Bandpass Filter 36
1.11.1 Example 1.6 37
1.12 Bandstop Filter 38
1.12.1 Example 1.7 40
1.13 1-D Digital Filters 41
1.14 Theory of Sampling 41
1.15 Design Procedures 49
1.16 Impulse Invariant Transformation 50
1.17 Bilinear Transformation 54
1.17.1 Example 1.8 56
1.17.2 Digital Spectral Transformation 60
1.17.3 Example 1.9 60
1.17.4 Example 1.10 64
1.18 Computer-Aided Optimization 64
1.19 Conclusion 65
2 Magnitude and Delay of I-D Filters 71
2.1 Introduction 71
2.2 Properties of an IIR Transfer Function 72
2.3 Maximally Flat Group Delay Filters 74
2.4 Simultaneous Approximation of Magnitude and Group Delay 83
2.4.1 Method 2.1: Nonlinear Optimization 83
2.4.2 Method 2.2 : Use of Mirror Image Polynomial 85
2.4.3 Method 2.3 : Maximally Flat Magnitude and Group Delay in the Passband 87
2.4.4 Design Theory 91
2.4.5 Example 2.1 94
2.4.6 Extension for an Equiripple Stopband Response 95
2.4.7 Remez Algorithm 97
2.4.8 Example 2.2 98
2.5 Design of Pulse Shaping Filters 99
2.5.1 Example 2.3 101
2.5.2 Method 2.4: Use of Allpass Sections in Parallel 104
2.5.3 Method 2.5: Use of Singular Value Decomposition 110
2.5.4 Example 2.4 113
2.5.5 Method 2.6: Application of Linear Programming 113
2.5.6 Method 2.7: Theory of Commensurate Distributed Networks 117
2.5.7 Equidistant Linear Phase Approximation 121
2.5.8 Method 2.8: Theory of Eigen Filters 122
2.5.9 Example 2.5 127
2.6 Conclusion 129
3 Magnitude of 2-D Filters 137
3.1 Introduction 137
3.2 Filters with Rectangular Passbands 138
3.3 Design of Fan Filters 151
3.3.1 Method 3.1 152
3.3.2 Example 3.1 154
3.3.3 Design of Fan Filters using Method 3.2 165
3.3.4 Design Procedure 166
3.3.5 Example 3.2 167
3.3.6 Method 3.3 168
3.3.7 Example 3.3 170
3.4 Design of Circularly Symmetric Filters 173
3.4.1 Survey of the literature 173
3.4.2 Design Procedures 175
3.5 Conclusion 182
4 Magnitude and Delay of 2-D Filters 187
4.1 Introduction 187
4.2 Design using Nonlinear Programming 188
4.2.1 Statement of the problem 188
4.2.2 Stability conditions 190
4.2.3 Design Examples 196
4.3 Design Using Linear Programming 213
4.4 Design Using Singular Value Decomposition 216
4.5 Chebyshev Approximation Theory 217
4.6 Design Using Digital Spectral Transformation 225
4.6.1 Example 4.5 233
4.6.2 Example 4.6 240
4.7 Conclusion 241
Index 249
END
