Contents v -- List of Figures ix -- List of Tables xv -- PREFACE xix -- ACKNOWLEDGMENTS xxi -- 1 ROAD MAP OF THE BOOK 1 -- 1.1 INTRODUCTION 1 -- 1.2 WHY USE WAVELETS? 1 -- 1.3 WHAT ARE WAVELETS? 2 -- 1.4 WHAT IS THE WAVELET TRANSFORM? 3 -- 1.5 USE OF WAVELETS IN THE NUMERICAL SOLUTION OF ELECTROMAGNETIC FIELD PROBLEMS 4 -- 1.6 WAVELET METHODOLOGIES COMPLEMENT FOURIER TECHNIQUES 7 -- 1.7 OVERVIEW OF THE CHAPTERS 10 -- REFERENCES 11 -- 2 WAVELETS FROM AN ELECTRICAL ENGINEERING PERSPECTIVE 15 -- 2.1 INTRODUCTION 15 -- 2.2 DEVELOPMENT OF THE DISCRETE WAVELET METHODOLOGY FROM FILTER THEORY CONCEPTS 16 -- 2.3 APPROXIMATION OF A FUNCTION BY WAVELETS 38 -- 2.4 EXAMPLES 43 -- 2.5 CONCLUSION 47 -- REFERENCES 47 -- APPENDIX 2A: Principles of Decimation and Expansion 48 -- 3 APPLICATION OF WAVELETS IN THE SOLUTION OF OPERATOR EQUATIONS 53 -- 3.1 INTRODUCTION 53 -- 3.2 APPROXIMATION OF A FUNCTION BY WAVELETS 59 -- 3.3 SOLUTION OF OPERATOR EQUATIONS 62 -- 3.4 WAVELET BASIS IN THE SOLUTION OF INTEGRAL EQUATIONS 64 -- REFERENCES 68 -- 4 SOLVING MATRIX EQUATIONS USING THE WAVELET TRANSFORM 71 -- 4.1 INTRODUCTION 71 -- 4.2 IMPLEMENTION OF THE WAVELET-LIKE TRANSFORM BASED ON THE TENSOR PRODUCT 75 -- 4.3 NUMERICAL EVALUATION OF THE WAVELET-LIKE TRANSFORM 80 -- 4.4 SOLUTION OF LARGE DENSE COMPLEX MATRIX EQUATIONS... 92 -- 4.5 UTILIZATION OF CUSTOM FIR FILTERS 102 -- 4.6 CONCLUSION 131 -- REFERENCES 132 -- 5 SOLVING THE DIFFERENTIAL FORM OF MAXWELL™ S EQUATIONS 135 -- 5.1 INTRODUCTION 135 -- 5.2 SOLUTION OF ONE-DIMENSIONAL PROBLEMS UTILIZING A WAVELET-LIKE BASIS 136 -- 5.3 SOLUTION OF Ñ 2 U + k 2 U = F FOR TWO-DIMENSIONAL PROBLEMS UTILIZING A WAVELET-LIKE BASIS 142 -- 5.4 APPLICATION TO SOME WAVEGUIDE PROBLEMS 146 -- 5.5 CONCLUSION 155 -- REFERENCES 155.

6 ADAPTIVE MULTISCALE MOMENT METHOD 157 -- 6.1 OVERVIEW 157 -- 6.2 INTRODUCTION OF THE MULTISCALING METHODOLOGY 158 -- 6.3 USE OF A MULTISCALE BASIS IN SOLVING INTEGRAL EQUATIONS VIA THE MOMENT METHOD (MM) 165 -- 6.4 DIFFERENCES BETWEEN A MULTISCALE BASIS AND A SUBDOMAIN TRIANGULAR BASIS ON AN INTERVAL [0, L] 171 -- 6.5 ANALYSIS OF ELECTROMAGNETIC SCATTERING FROM MATERIALLY COATED STRIPS 174 -- 6.6 EXTENSION OF THE MULTISCALE CONCEPTS TO 2-D PROBLEMS 199 -- 6.7 A TWO-DIMENSIONAL MULTISCALE BASIS ON A TRIANGULAR DOMAIN... 227 -- 6.8 DISCUSSION 244 -- 6.9 CONCLUSION 245 -- REFERENCES 246 -- 7 THE CONTINUOUS WAVELET TRANSFORM AND ITS RELATIONSHIP TO THE FOURIER TRANSFORM 247 -- 7.1 INTRODUCTION 247 -- 7.2 CONTINUOUS TRANSFORMS 248 -- 7.3 DISCRETE TRANSFORMS 257 -- 7.4 CONCLUSION 271 -- REFERENCES 271 -- 8 T-PULSE: WINDOWS THAT ARE STRICTLY TIME LIMITED AND PRACTICALLY BAND LIMITED 273 -- 8.1 INTRODUCTION 273 -- 8.2 A DISCUSSION ON VARIOUS CHOICES OF THE WINDOW FUNCTION 274 -- 8.3 DEVELOPMENT OF THE T-PULSE 275 -- 8.4 SUMMARY OF THE OPTIMIZATION TECHNIQUES 278 -- 8.5 NUMERICAL RESULTS 280 -- 8.6 CONCLUSION 293 -- REFERENCES 293 -- 9 OPTIMAL SELECTION OF A SIGNAL-DEPENDENT BASIS AND DENOISING 295 -- 9.1 INTRODUCTION 295 -- 9.2 SELECTION OF AN OPTIMUM BASIS 295 -- 9.3 DENOISING OF SIGNALS THROUGH THE WAVELET TRANSFORM 301 -- 9.4 CONCLUSION 303 -- REFERENCES 304 -- SELECTED BIBLIOGRAPHY 305 -- BOOKS 305 -- JOURNAL AND CONFERENCE PAPERS 306 -- ABOUT THE AUTHORS 331 -- Index 337.