# An Introduction to Wavelet Analysis

Springer Science & Business Media, 2002 - 449 Seiten

"D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!"

—Bulletin of the AMS

An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases.

The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical prerequisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts.

Features:

* Rigorous proofs with consistent assumptions about the mathematical background of the reader (does not assume familiarity with Hilbert spaces or Lebesgue measure).

* Complete background material on is offered on Fourier analysis topics.

* Wavelets are presented first on the continuous domain and later restricted to the discrete domain for improved motivation and understanding of discrete wavelet transforms and applications.

* Special appendix, "Excursions in Wavelet Theory, " provides a guide to current literature on the topic.

* Over 170 exercises guide the reader through the text.

An Introduction to Wavelet Analysis is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference guide for professionals.

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### Inhalt

 III 3 IV 6 V 9 VI 11 VII 13 VIII 14 IX 17 X 19
 LXXXII 208 LXXXIII 215 LXXXIV 218 LXXXVI 221 LXXXVII 223 LXXXVIII 231 LXXXIX 232 XC 236

 XI 21 XII 27 XIII 28 XIV 30 XV 32 XVI 37 XVII 38 XVIII 40 XIX 42 XX 47 XXI 49 XXII 52 XXIII 59 XXIV 63 XXV 65 XXVI 68 XXVII 72 XXVIII 75 XXIX 76 XXX 79 XXXI 81 XXXII 87 XXXIII 88 XXXIV 90 XXXV 95 XXXVI 101 XXXVII 102 XXXVIII 107 XXXIX 109 XL 113 XLI 115 XLII 116 XLIII 117 XLIV 118 XLV 120 XLVI 122 XLVII 127 XLVIII 128 XLIX 130 L 132 LI 133 LII 134 LIII 138 LV 141 LVI 142 LVII 146 LIX 147 LX 150 LXI 151 LXII 153 LXIII 154 LXIV 161 LXV 163 LXVI 164 LXVII 169 LXVIII 170 LXIX 174 LXX 179 LXXI 180 LXXII 185 LXXIII 186 LXXIV 190 LXXV 193 LXXVI 196 LXXVII 197 LXXVIII 199 LXXIX 203 LXXX 206
 XCI 237 XCII 243 XCIII 245 XCIV 249 XCV 250 XCVI 254 XCVII 257 XCVIII 260 XCIX 264 CI 269 CII 277 CIII 278 CV 285 CVI 287 CVII 288 CVIII 291 CIX 300 CX 301 CXI 302 CXII 311 CXIII 313 CXIV 315 CXVI 317 CXVII 319 CXVIII 320 CXIX 324 CXX 328 CXXI 335 CXXII 337 CXXIII 338 CXXIV 346 CXXV 347 CXXVI 350 CXXVII 354 CXXX 357 CXXXI 360 CXXXII 363 CXXXIII 369 CXXXIV 371 CXXXV 372 CXXXVI 373 CXXXVIII 375 CXXXIX 376 CXL 378 CXLI 380 CXLII 385 CXLIII 387 CXLIV 388 CXLV 397 CXLVI 402 CXLVII 406 CXLVIII 414 CXLIX 415 CL 418 CLI 423 CLII 425 CLIII 431 CLIV 433 CLV 434 CLVII 435 CLVIII 436 CLX 437 CLXI 438 CLXIII 439 CLXIV 441 CLXV 445 Urheberrecht