Modern sampling theory mathematics and applications
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|---|---|
| Sprache: | English |
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Boston ; Basel ; Berlin
Birkhäuser
2001
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| Schriftenreihe: | Applied and numerical harmonic analysis
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| 245 | 1 | 0 | |a Modern sampling theory |b mathematics and applications |c John J. Benedetto ... eds. |
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 2001 | |
| 300 | |a XVI, 417 S. |b Ill., graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Applied and numerical harmonic analysis | |
| 500 | |a Literaturverz. S. 379 - 413 | ||
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| 650 | 4 | |a Sampling (Statistics) | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102/MAT 629f 2001 A 1695 |
|---|---|
| DE-BY-TUM_katkey | 1424351 |
| DE-BY-TUM_media_number | 040020113619 |
| _version_ | 1816712300124438528 |
| adam_text | MODERN SAMPLING THEORY MATHEMATICS AND APPLICATIONS JOHN J. BENEDETTO
PAULO J.S.G. FERREIRA EDITORS WITH 37 FIGURES BIRKHAUSER BOSTON * BASEL
* BERLIN CONTENTS PREFACE XI CONTRIBUTORS XIII 1 INTRODUCTION 1 JOHN J.
BENEDETTO AND PAULO J. S. G. FERREIRA 1.1 THE CLASSICAL SAMPLING THEOREM
1 1.2 NON-UNIFORM SAMPLING AND FRAMES 10 1.3 OUTLINE OF THE BOOK 21
1.3.1 SAMPLING, WAVELETS, AND THE UNCERTAINTY PRINCIPLE 22 1.3.2
SAMPLING TOPICS FROM MATHEMATICAL ANALYSIS . . . . 23 1.3.3 SAMPLING
TOOLS AND APPLICATIONS 24 2 ON THE TRANSMISSION CAPACITY OF THE ETHER
AND WIRE IN ELECTROCOMMUNICATIONS 27 V. A. KOTEL NIKOV (TRANSLATED BY V.
E. KATSNELSON) I SAMPLING, WAVELETS, AND THE UNCERTAINTY PRINCIPLE 47 3
WAVELETS AND SAMPLING 49 GILBERT G. WALTER 3.1 INTRODUCTION 49 3.1.1
BACKGROUND 49 3.1.2 THE RKHS SETTING 50 3.1.3 THE WAVELET SETTING 51 3.2
SAMPLING IN OTHER SPACES 52 3.2.1 IMPULSE TRAIN CONVERGENCE 53 3.2.2
RKHS AND SAMPLING 57 3.3 SAMPLING IN WAVELET SUBSPACES 58 3.3.1 ELEMENTS
OF WAVELET THEORY 58 3.3.2 SAMPLING FUNCTIONS 60 3.3.3 SAMPLED VALUES AS
COEFFICIENTS 63 3.4 INTERPOLATING MULTIWAVELETS 66 3.4.1 PROPERTIES OF
HERMITE SAMPLING FUNCTIONS 67 CONTENTS EMBEDDINGS AND UNCERTAINTY
PRINCIPLES FOR GENERALIZED MODULATION SPACES 73 J. A. HOGAN AND J. D.
LAKEY 4.1 INTRODUCTION 73 4.1.1 WEIGHTED FOURIER INEQUALITIES IMPLY
UNCERTAINTY PRINCIPLE INEQUALITIES 75 4.1.2 SHARP CONSTANTS AND ENDPOINT
ESTIMATES 76 4.1.3 EMBEDDINGS FOR MODULATION SPACES 77 4.2 THE
SHORT-TIME FOURIER TRANSFORM AND MODULATION SPACES 77 4.2.1 WEIGHTED
FOURIER INEQUALITIES IMPLY MODULATION EMBEDDINGS 80 4.2.2 REPRESENTATION
THEORY AND THE LINK WITH LITTLEWOOD- PALEY THEORY 81 4.2.3 MORE REMARKS
ON THE UNCERTAINTY PRINCIPLE 82 4.3 MODULATION EMBEDDINGS AND
UNCERTAINTY PRINCIPLES .... 82 4.3.1 GROCHENIG S TWO-SIDED EMBEDDING
THEOREM .... 82 4.3.2 LIEB S SHARP SINGLE-SIDED EMBEDDING THEOREM ... 88
4.4 SYMMETRIC LOCALIZATION 89 4.5 GENERALIZED MODULATION SPACES 93 4.5.1
GENERALIZED SQUARE-INTEGRABILITY, FRAMES, AND THE METAPLECTIC GROUP 94
4.5.2 THE METAPLECTIC GROUP 95 4.5.3 GENERALIZED SQUARE INTEGRABILITY 96
4.5.4 CONNECTION WITH TIME-FREQUENCY LOCALIZATION ... 97 4.5.5
METAPLECTIC FRAMES 97 4.6 GENERALIZED MODULATION SPACES AND EMBEDDING
100 SAMPLING THEORY FOR CERTAIN HILBERT SPACES OF BANDLIMITED FUNCTIONS
107 JEAN-PIERRE GABARDO 5.1 INTRODUCTION 107 5.2 NOTATION 108 5.3
POSITIVE-DEFINITE DISTRIBUTIONS ON (-R, R) 109 5.4 THE CASE WHERE A4R(H)
HAS FINITE CODIMENSION IN L^ . . 115 5.5 THE GENERAL CASE 129 5.6 RIESZ
BASES AND FRAMES 134 SHANNON-TYPE WAVELETS AND THE CONVERGENCE OF THEIR
ASSOCIATED WAVELET SERIES 135 AHMED I. ZAYED 6.1 INTRODUCTION 135 6.2
PRELIMINARIES 136 6.3 SHANNON S WAVELET 138 6.4 GENERALIZED SHANNON
WAVELETS 140 6.5 POINTWISE CONVERGENCE OF SHANNON-TYPE WAVELET SERIES .
. . 147 CONTENTS VII II SAMPLING TOPICS FROM MATHEMATICAL ANALYSIS 153 7
NON-UNIFORM SAMPLING IN HIGHER DIMENSIONS: FROM TRIGONOMETRIC
POLYNOMIALS TO BANDLIMITED FUNCTIONS 155 KARLHEINZ GROCHENIG 7.1
INTRODUCTION 155 7.2 NON-UNIFORM SAMPLING WITH TRIGONOMETRIC POLYNOMIALS
. . 157 7.3 TOWARD BANDLIMITED FUNCTIONS 161 7.4 PROOF OF THEOREM 7.1
167 8 THE ANALYSIS OF OSCILLATORY BEHAVIOR IN SIGNALS THROUGH THEIR
SAMPLES 173 RODOLFO H. TORRES 8.1 INTRODUCTION AND MOTIVATION 173 8.2
BESOV SPACES OF FUNCTIONS 178 8.3 SAMPLING THEOREM FOR BESOV SPACES AND
THEIR DISCRETE COUNTERPART 182 8.4 OTHER CHARACTERIZATIONS OF THE
DISCRETE BESOV SPACES . . . 185 8.5 NONLINEAR APPROXIMATION OF BAND
LIMITED SIGNALS USING SAMPLES 188 8.6 CONCLUDING REMARKS 192 9 RESIDUE
AND SAMPLING TECHNIQUES IN DECONVOLUTION 193 STEPHEN CASEY AND DAVID
WALNUT 9.1 INTRODUCTION 193 9.1.1 STATEMENT OF THE PROBLEM 193 9.1.2 THE
COPRIME CONDITION AND LOCAL DECONVOLUTION . . 194 9.1.3 OTHER TYPES OF
DECONVOLVERS 195 9.1.4 EXAMPLE: CUBES IN R D 196 9.1.5 EXAMPLE: BALLS IN
R D 197 9.1.6 PRACTICAL DECONVOLUTION 198 9.2 RESIDUE METHODS FOR
DECONVOLUTION 199 9.3 SAMPLING METHODS FOR DECONVOLUTION 209 9.3.1
DECONVOLUTION AND SETS OF UNIQUENESS IN C M - 2 [-R,R] 210 9.3.2
NONPERIODIC FRAMES AND BASES FOR L 2 [*R, R] .... 215 9.3.3
DECONVOLUTION AND THE COMPLETENESS OF T 217 10 SAMPLING THEOREMS FROM
THE ITERATION OF LOW ORDER DIFFERENTIAL OPERATORS 219 J. R. HLGGINS 10.1
INTRODUCTION 219 10.2 PRELIMINARY FACTS AND METHODS 220 10.3 EXAMPLES OF
THE METHOD 223 10.4 REMARKS AND OPEN PROBLEMS 227 VIII CONTENTS 11
APPROXIMATION OF CONTINUOUS FUNCTIONS BY ROGOSINSKI* TYPE SAMPLING
SERIES 229 ANDI KIVINUKK 11.1 NOTATION AND INTRODUCTION TO THE SAMPLING
SERIES 229 11.2 ROGOSINSKI*TYPE SAMPLING SERIES 232 11.3 APPLICATIONS TO
GENERALIZED SAMPLING SERIES 239 11.4 CONCLUSION 244 III SAMPLING TOOLS
AND APPLICATIONS 245 12 FAST FOURIER TRANSFORMS FOR NONEQUISPACED DATA:
A TUTORIAL 247 DANIEL POTTS, GABRIELE STEIDL, AND MANFRED TASCHE 12.1
INTRODUCTION 247 12.2 NDFT FOR NONEQUISPACED DATA EITHER IN TIME OR
FREQUENCY DOMAIN 250 12.3 NDFT FOR NONEQUISPACED DATA IN TIME AND
FREQUENCY DOMAIN 258 12.4 ROUNDOFF ERRORS 261 12.5 FAST BESSEL TRANSFORM
265 13 EFFICIENT MINIMUM RATE SAMPLING OF SIGNALS WITH FREQUEN- CY
SUPPORT OVER NON-COMMENSURABLE SETS 271 CORMAC HERLEY AND PING WAH WONG
13.1 INTRODUCTION 271 13.2 PERIODIC NON-UNIFORM SAMPLING 273 13.3
RECONSTRUCTION OF A DISCRETE-TIME SIGNAL FROM N SAMPLES OUT OF M 275
13.4 FILTER DESIGN USING POCS 283 13.5 MINIMUM RATE SAMPLING OF
MULTIBAND SIGNALS 284 13.6 SLICING THE SPECTRUM 288 13.6.1 DIVIDING THE
BANDS INTO SLICES 290 13.6.2 FREEDOM IN PAIRING 290 13.6.3 PAIRING THE
EDGES 291 14 FINITE- AND INFINITE-DIMENSIONAL MODELS FOR OVERSAMPLED
FILTER BANKS 293 THOMAS STROHMER 14.1 INTRODUCTION 293 14.1.1
OVERSAMPLED FILTER BANKS AND FRAMES 295 14.2 FINITE-DIMENSIONAL MODELS
FOR FILTER BANKS 296 14.2.1 THE FINITE SECTION METHOD FOR OVERSAMPLED
FILTER BANKS 297 CONTENTS IX 14.2.2 FINITE SECTIONS, LAURENT OPERATORS,
AND POLYPHASE MATRICES 298 14.2.3 POLYPHASE MATRICES AND PERFECT SYMBOL
CALCULUS IN FINITE DIMENSIONS 300 14.3 CONVERGENCE AND RATES OF
APPROXIMATION FOR FINITE DIMENSIONAL APPROXIMATIONS . . . 301 14.3.1
RATES OF APPROXIMATION FOR OVERSAMPLED FILTER BANKS 302 14.4 CONVERGENCE
USING POLYPHASE REPRESENTATION 305 14.5 FINITE-DIMENSIONAL APPROXIMATION
OF PARAUNITARY FILTER BANKS VIA 5 2 309 14.6 OVERSAMPLED DFT FILTER
BANKS * BEYOND POLYPHASE REPRESENTATION 311 14.6.1 MATRIX FACTORIZATION
OF THE FRAME OPERATOR 312 15 STATISTICAL ASPECTS OF SAMPLING FOR NOISY
AND GROUPED DA- TA 317 M. PAWLAK AND U. STADTMULLER 15.1 INTRODUCTION
317 15.2 SAMPLING FROM NOISY DATA AND SIGNAL RECOVERY 319 15.3 SIGNAL
RECOVERY FROM GROUPED DATA 324 15.4 STATISTICAL ACCURACY 327 15.5
CONCLUDING REMARKS 334 15.6 PROOFS 336 16 RECONSTRUCTION OF MRI IMAGES
FROM NON-UNIFORM SAMPLING AND ITS APPLICATION TO INTRASCAN MOTION
CORRECTION IN FUNCTIONAL MRI 343 MARC BOURGEOIS, FRANK T. A. W. WAJER,
DIRK VAN ORMONDT, AND DANIELLE GRAVERON-DEMILLY 16.1 INTRODUCTION 343
16.2 MRI SAMPLING TRAJECTORIES 344 16.3 MOTION INFLUENCE AND CORRECTION
OF INTRASCAN MOTION ARTIFACTS 346 16.3.1 PHYSIOLOGICAL AND SUBJECT
MOTIONS 346 16.3.2 REDUCTION OF MOTION ARTIFACTS IN IMAGES 347 16.3.3
CORRECTION OF INTRASCAN MOTIONS IN FMRI 347 16.4 IMAGE RECONSTRUCTION
FROM NON-UNIFORM SAMPLING 350 16.4.1 GRIDDING FROM A NON-UNIFORM GRID TO
A CARTESIAN GRID AND VICE VERSA 350 16.4.2 DENSITY CORRECTION AND
VORONOI ALGORITHM 351 16.4.3 LIMITS OF GRIDDING 352 16.5 BAYESIAN IMAGE
ESTIMATION 353 16.5.1 PREAMBLE 353 16.5.2 THE MOST PROBABLE IMAGE 354 X
CONTENTS 16.5.3 THE LIKELIHOOD 355 16.5.4 THE PRIOR 355 16.5.5
CALCULATION OF TI 358 16.6 APPLICATIONS OF INTRASCAN MOTION CORRECTION
TO FMRI . . . . 358 16.6.1 SHEPP-LOGAN SIMULATION 358 16.6.2 SIMULATED
FMRI EXPERIMENT 359 16.7 CONCLUSIONS 362 17 EFFICIENT SAMPLING OF THE
ROTATION INVARIANT RADON TRANSFORM 365 LAURENT DESBAT AND CATHERINE
MENNESSIER 17.1 INTRODUCTION 365 17.1.1 PRINCIPLE 365 17.1.2 INVERSE
PROBLEM FORMALISM 366 17.2 EFFICIENT SAMPLING IN 2D TOMOGRAPHY 369
17.2.1 RESULTS IN STANDARD TOMOGRAPHY 369 17.2.2 GENERALIZATION TO THE
ROTATION INVARIANT RADON TRANSFORM 371 17.3 APPLICATION TO DOPPLER
IMAGING 374 17.3.1 NULL INCLINATION CASE: A = 0 374 17.3.2 PERPENDICULAR
INCLINATION CASE: A = IR/2 374 17.4 DISCUSSION 376 REFERENCES 379 INDEX
414
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| id | DE-604.BV013758768 |
| illustrated | Illustrated |
| indexdate | 2024-11-25T17:19:56Z |
| institution | BVB |
| isbn | 9780817640231 3764340231 0817640231 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009406101 |
| oclc_num | 44681881 |
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| physical | XVI, 417 S. Ill., graph. Darst. : 24 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Applied and numerical harmonic analysis |
| spellingShingle | Modern sampling theory mathematics and applications Échantillonnage (Statistique) Sampling (Statistics) Stichprobe (DE-588)4057502-0 gnd |
| subject_GND | (DE-588)4057502-0 (DE-588)4143413-4 |
| title | Modern sampling theory mathematics and applications |
| title_auth | Modern sampling theory mathematics and applications |
| title_exact_search | Modern sampling theory mathematics and applications |
| title_full | Modern sampling theory mathematics and applications John J. Benedetto ... eds. |
| title_fullStr | Modern sampling theory mathematics and applications John J. Benedetto ... eds. |
| title_full_unstemmed | Modern sampling theory mathematics and applications John J. Benedetto ... eds. |
| title_short | Modern sampling theory |
| title_sort | modern sampling theory mathematics and applications |
| title_sub | mathematics and applications |
| topic | Échantillonnage (Statistique) Sampling (Statistics) Stichprobe (DE-588)4057502-0 gnd |
| topic_facet | Échantillonnage (Statistique) Sampling (Statistics) Stichprobe Aufsatzsammlung |
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