A Unified Signal Algebra Approach to Two-Dimensional Parallel Digital Signal Processing: Volume 210: D'Alotto; Louis A.: 9780824700256: Book: Technology: eCampus.com

Reference/text offers a modern approach to digital signal processing utilizing the unified signal algebra environment, developed in the text, to construct naturally occurring parallel DSP algorithms. DLC: Signal processing - digital.

Preface

1 Two Dimensional Signals

(16)

1.1 Two Dimensional Digital Signals

(4)

1.2 Important Two Dimensional Digital Signals

(3)

1.3 Bound Matrix Representation

(6)

1.4 Exercises

(3)

2 Fundamental Operations on Two Dimensional Signals

(42)

2.1 Fundamental Range Induced Operations

(3)

2.2 Terms Involving Fundamental Range Induced Operations

(6)

2.3 Additional Important Digital Signals and Macro Operators

(3)

2.4 Equational Identities Involving Range Induced Operations

(6)

2.5 Fundamental Domain Induced Operations

(7)

2.6 Terms Involving Fundamental Domain Induced Operations

(8)

2.7 Further Equational Identities

(3)

2.8 Exercises

(6)

3 Convolution of Digital Signals

(56)

3.1 The Support Region for Convolution

(2)

3.2 Convolution for Signals of Finite Support

(4)

3.3 Bound Matrices for Convolution

(3)

3.4 Parallel Convolution Algorithms

(5)

3.5 Convolution of Signals of Non-Finite Support

(6)

3.6 Banach Algebra Properties of Convolution in l(1)

(4)

3.7 Filtering by Convolution

(9)

3.8 Correlation

(11)

3.9 Applications of Correlation

103

(6)

3.10 Exercises

109

(6)

4 Z Transforms

115

(44)

4.1 Formal Introduction to Z Transforms

115

(3)

4.2 Some Operations Involving Z Transforms

118

(7)

4.3 Z Transforms for Digital Signals of Finite Support

125

(4)

4.4 Laurent Expansions

129

(14)

4.5 Z Transform for l(1) Signals and Signals of Arbitrary Support

143

(3)

4.6 The Z Transform for Calculating Correlation

146

(2)

4.7 Transfer Functions

148

(5)

4.8 Exercises

153

(6)

5 Difference Equations

159

(28)

5.1 Function Equations

159

(2)

5.2 Linear Space Invariant Difference Equations

161

(7)

5.3 Difference Equations Involving One Unit Translation

168

(10)

5.4 Z Transforms for Solving Difference Equations

178

(7)

5.5 Exercises

185

(2)

6 Wraparound Signal Processing

187

(62)

6.1 Wraparound Signals

187

(3)

6.2 Range Induced Operations and Terms for Wraparound Signals

190

(5)

6.3 Domain Induced Operations for Wraparound Signals

195

(9)

6.4 Set Morphology in Z(n) x Z(m)

204

(8)

6.5 Sequential and Parallel Formulation of Wraparound Convolution

212

(6)

6.6 Sequential and Parallel Formulations of Wraparound Correlation

218

(5)

6.7 Wraparound Z Transforms

223

(7)

6.8 Discrete Fourier Transforms

230

(4)

6.9 Wraparound Algebra in Z(n) x Z(m)

234

(9)

6.10 Exercises

243

(6)

7 Parallel Multidimensional Algorithms for Single Dimensional Signal Processing

249

(30)

7.1 Two Dimensional Processing of One Dimensional Signals

249

(3)

7.2 Diagonal Transform from One Dimension into Two Dimensions

252

(2)

7.3 Kronecker Products

254

(5)

7.4 Triple Convolution

259

(2)

7.5 Triple Convolution Performed Using Parallel Two Dimensional Convolution

261

(4)

7.6 Volterra Convolution and Volterra Series

265

(4)

7.7 Parallel Algorithms for Volterra Convolution

269

(6)

7.8 Exercises

275

(4)

Appendix

279

(8)

References

287


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