Wavelet Theory And Its Applications Book

	Foreword
	Preface
Ch. 1	Introduction/Background	1
	Wavelet Theory Basics - Scaling and Translation	4
	Appendix 1-A: Time Referencing	16
Ch. 2	The Wavelet Transform	19
	Wavelet Transform Definitions and Operators	19
	Wavelet Transform Examples	22
	The Resolution of Identity	27
	Continuous Inverse Wavelet Transform Theorem	30
	Energy Distribution in the Wavelet Transform Domain	34
	Discrete Wavelet Transform (Continuous Time Wavelet Series)	35
	Wideband Matched Filter Interpretation of the Lattice Density	38
	Review of the Inverse Discrete Wavelet Transform: Scale-translation Lattice Density and Mother Wavelet Constraints	41
	Discrete Wavelet Mathematics - Rigorous Justification	44
	Discrete Time Wavelet Series	50
	Multiresolution, Orthogonal, and Biorthogonal Wavelet Transforms (and PR-QMFs)	51
	Discrete Time Wavelet Series - A Specific Structure	52
	Multiresolution	55
	Orthogonal and Biorthogonal Wavelet Transforms	57
	An Image Processing Example	60
	Appendix 2-A: Nonunique Wavelet Domain Representations	64
Ch. 3	Practical Resolution, Gain, and Processing Structures	71
	Fourier/Narrowband Gain and Resolution Comparisons	72
	Multiple Mother Wavelets - Gain and Resolution Properties Only	77
	Mother Wavelet Properties - Relationships to Established Theories	79
	Signal Analysis - Time-frequency or time-scale Applications	80
	A Physical Interpretation of Scale-translation Resolution: Wideband Ambiguity Function Conditions	81
	Wideband Conditions	82
	Wideband Signals and the Analytic Signal Model	83
	Effective rms Time-bandwidth Product	85
	Wideband Systems and Signals	87
	Active and Passive Sensing	92
	Ambiguity Functions	95
	Reformulation of the WBCAF with Wavelet Transforms	101
	Properties of the Reformulated WBCAF	105
	Cross Wavelet Transforms and Signal Commonalities	110
	Appendix 3-A: Wideband/Narrowband Ambiguity Functions: Assumptions, Tradeoffs and Efficiencies	113
	Appendix 3-B: Narrowband Ambiguity Function Theory	119
Ch. 4	Wavelet Theory Extensions and Ambiguity Functions	123
	Multiresolution/Orthogonal Wavelets versus Unconstrained Wavelets	123
	Sampling Grids	126
	Unconstrained Wavelet Transforms - Mother Wavelet Freedom	127
	The Mother Mapper Operator	128
	Unconstrained Wavelet Transforms/Mother Mapper Operator Properties and Applications	133
	Mother Mapper Operator Applications	137
	Mother Mapper Operator - Final Considerations	139
	Further Research and Applications of the Mother Mapper Operator	140
Ch. 5	Linear Systems Modelling with Wavelet Theory	141
	Wideband/Nonstationary/Time-varying System Modelling	143
	The Wideband Signal Reflection Process	146
	Common Framework of System or Channel Characterizations	151
	The STV Wavelet Operator - Space-time-varying System Model	156
	STV Wavelet Operator's Energy Distribution	159
	Estimation of the Wideband System Characterization	160
	Properties of the STV Wavelet Operator	160
	Examples of the STV Wavelet Operator	164
	Wideband Reflection: Comparing the LTI and STV Models	169
	Justification for the STV Operator Instead of Convolution for Signals Represented by Wavelet Transforms	174
	The STV Wavelet Operator in the Wavelet Transform Domain	175
	Space-time-varying System Identification Problem with Wideband/Nonstationary Input/Outputs	180
	Limitations of the STV Wavelet Operator - Time Referencing and Nonlinear Time Variations	181
	Bi-wavelet System Representation: Time variation of the Time-varying System Model	184
Ch. 6	Wideband Scattering and Environmental Imaging	189
	Scattering Theory	192
	General Scattering Function Background	193
	Narrowband Scattering Theory	194
	Wideband Correlation Receiver and its Output	198
	Wideband Point Scatterer Example	201
	Wideband Scattering Functions and Resolutions	203
	Physical Form of the WBCAF	205
	Time Delay and Scale Estimation	208
	WBAAF Moments and Assumptions	209
	Wideband Scattering Review	210
	Related Research	211
	References	215
	Subject Index	221