Information Theory

Analysis and Probability: Wavelets, Signals, Fractals by Palle E. T. Jorgensen, B. Treadway

By Palle E. T. Jorgensen, B. Treadway

Combines research and instruments from probability, harmonic research, operator thought, and engineering (signal/image processing)

Interdisciplinary focus with hands-on strategy, beneficiant motivation and new pedagogical techniques

Numerous workouts strengthen basic strategies and hone computational skills

Separate sections clarify engineering phrases to mathematicians and operator concept to engineers

Fills a spot within the literature

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Additional resources for Analysis and Probability: Wavelets, Signals, Fractals (Graduate Texts in Mathematics)

Example text

2(b), is Z^-normalized, but not L^-normalized. 24). ,: "-"-f;"' '•'—^—' H T ^-•" "-^ ¥ 1 / 0 -1 Fig. 2. , the mother functions for Haar's construction in cases (a) on the left, and the stretched Haar (b), on the right. 16). 22) for every function in L^(R). As is apparent from (b), this Parseval system will not be an ONB for the stretched version. 1 (p. 103). 24) get lost. 23). 24). 14 1 Introduction: Measures on path space For (a), we may take (P = ^ a = X [ 0 , l ] ' and for (b), 1 (P=^(ph= 3/[0,3]' where / denotes the indicator function of the respective intervals.

And they progress in logical steps, often with one part building on the previous, hi all, the exercises make up more than 40 pages. We have presented the material so that different readers can select the parts of it that are closest to his/her own interests; and in particular, it is not necessary to begin with Chapter 1. Li fact, for some it might be better to begin with the Appendices, or with the Afterword containing the special sections "Comments on signal/image processing terminology" and "Computational mathematics," or for some insight into the history of the subject, the "List of names and discoveries" on pages xxx-xxxiii above.

JaMROl, Mey89, MeCo97, Mey97] 1989 Albert Cohen mathematics (orthogonality relations), numerical analysis Discovered the use of wavelet filters in the analysis of wavelets—^the so-called Cohen condition for orthogonality. Chapters 5,6 [Coh90, Dau92, Law91a, Law91b] 1986 Stephane Mallat mathematics, signal and image processing While still a graduate student in engineering, working on vision, and on the Littlewood-Paley octaves, formalized and discovered what is now known as the subdivision, and multiresolution method, as well as the subdivision wavelet algorithms.

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