LEADER 05419nam 2200697Ia 450 001 9910807912503321 005 20240313221825.0 010 $a1-281-91871-7 010 $a9786611918712 010 $a981-270-908-8 035 $a(CKB)1000000000414173 035 $a(EBL)1193154 035 $a(SSID)ssj0000297182 035 $a(PQKBManifestationID)12094239 035 $a(PQKBTitleCode)TC0000297182 035 $a(PQKBWorkID)10332783 035 $a(PQKB)10968137 035 $a(MiAaPQ)EBC1193154 035 $a(WSP)00006541 035 $a(Au-PeEL)EBL1193154 035 $a(CaPaEBR)ebr10698854 035 $a(CaONFJC)MIL191871 035 $a(OCoLC)820944287 035 $a(EXLCZ)991000000000414173 100 $a20070510d2007 uy 0 101 0 $aeng 135 $aurbuu---unuuu 181 $ctxt 182 $cc 183 $acr 200 00$aGabor and wavelet frames /$feditors, Say Song Goh, Amos Ron, Zuowei Shen 205 $a1st ed. 210 $aHackensack, NJ $cWorld Scientific$dc2007 215 $a1 online resource (228 p.) 225 1 $aLecture notes series,$x1793-0758 ;$vv. 10 300 $aDescription based upon print version of record. 311 $a981-270-907-X 320 $aIncludes bibliographical references. 327 $aCONTENTS; Foreword; Preface; A Guided Tour from Linear Algebra to the Foundations of Gabor Analysis Hans G. Feichtinger, Franz Luef and Tobias Werther; 1. Introduction; 2. Basics in Linear Algebra; 3. Finite Dimensional Gabor Analysis; 4. Frames and Riesz Bases; 5. Gabor Analysis on L2; 6. Time-Frequency Representations; 7. The Gelfand Triple; 8. The Spreading Function; 9. Conclusion and Outlook; References; Some Iterative Algorithms to Compute Canonical Windows for Gabor Frames A. J. E. M. Janssen; 1. Introduction; 2. Overview; 3. Basic Tools; 4. Analysis of Recursion I to Approximate gt 327 $a5. Proposing Iterations Without Inversions 5.1. Iterations for gt; 5.2. Iterations for gd; 6. Analysis of Recursion II to Approximate gt; 7. Analysis of Recursion IV to Approximate gd; 8. Summary of Results for Iterations III and V; 9. Concluding Remarks; Acknowledgments; References; Gabor Analysis, Noncommutative Tori and Feichtinger's Algebra Franz Luef; 1. Introduction; 2. Operator Algebras of Time-Frequency Shifts; 3. Noncommutative Tori and Feichtinger's Algebra; 4. Feichtinger's Algebra as Bimodule for C ( ) and C ( 0) 327 $a5. Application to Gabor Analysis: Biorthogonality Relation of Wexler-Raz 6. Conclusions; Acknowledgment; References; Unitary Matrix Functions,Wavelet Algorithms, and Structural Properties of Wavelets Palle E. T. Jorgensen; 1. Introduction; 1.1. Index of terminology in mathematics and in engineering; 1.2. Motivation; 1.2.1. Some points of history; 1.2.2. Some early applications; 2. Signal Processing; 2.1. Filters in communications engineering; 2.2. Algorithms for signals and for wavelets; 2.2.2. Subdivision algorithms; 2.2.3. Wavelet packet algorithms 327 $a2.2.4. Lifting algorithms: Sweldens and more 2.3. Factorization theorems for matrix functions; 2.3.1. The case of polynomial functions [the polyphase matrix, joint work with Ola Bratteli]; 2.3.2. General results in mathematics on matrix functions; 2.3.3. Connection between matrix functions and wavelets; 2.3.3.1. Multiresolution wavelets; 2.3.3.2. Generalized multiresolutions [joint work with L. Baggett, K. Merrill, and J. Packer]; 2.3.4. Matrix completion; 2.3.5. Connections between matrix functions and signal processing; Acknowledgments; References 327 $aUnitary Systems, Wavelet Sets, and Operator-Theoretic Interpolation of Wavelets and Frames David R. Larson 1. Introduction; 1.1. Talks and abstracts; 1.2. Some background; 1.2.1. Interpolation; 1.2.2. Some basic terminology; 1.2.3. Acknowledgements; 2. Unitary Systems and Wavelet Sets; 2.1. The one-dimensional wavelet system; 2.1.1. Dyadic wavelets; 2.1.2. The dyadic unitary system; 2.1.3. Non-dyadic wavelets in one dimension; 2.2. N dimensions; 2.2.1. The expansive-dilation case; 2.2.2. The non-expansive dilation case; 2.3. Abstract systems; 2.3.1. Restrictions on wandering vectors 327 $a2.3.2. Group systems 330 $aGabor and wavelet analyses have found widespread applications in signal analysis, image processing and many other information-related areas. Both deliver representations that are simultaneously local in time and in frequency. Due to their significance and success in practical applications, they formed some of the core topics of the program "Mathematics and Computation in Imaging Science and Information Processing", which was held at the Institute for Mathematical Sciences, National University of Singapore, from July to December 2003 and in August 2004. As part of the program, tutorial lectures 410 0$aLecture notes series (National University of Singapore. Institute for Mathematical Sciences) ;$vv. 10. 606 $aGabor transforms 606 $aWavelets (Mathematics) 615 0$aGabor transforms. 615 0$aWavelets (Mathematics) 676 $a515/.723 701 $aGoh$b Say Song$01657977 701 $aRon$b Amos$0863332 701 $aShen$b Zuowei$01657978 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910807912503321 996 $aGabor and wavelet frames$94011720 997 $aUNINA