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

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 procedure, beneficiant motivation and new pedagogical techniques

Numerous workouts make stronger basic strategies and hone computational skills

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

Fills a niche within the literature

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Additional info for Analysis and Probability Wavelets, Signals, Fractals

Sample text

2 below. Chapter 2 develops general theory, transition probabilities, branching processes, and corresponding probability spaces. This material has a more technical flavor. hi Chapter 3 we specialize the measures, constructed in a general fi-amework in Chapter 2, to the concrete context of wavelets in the Hilbert space Z^(E). hi Chapter 2, we introduced transition probabilities Px on a probability space Q; and in the wavelet application, we outline how the group of integers Z is naturally embedded in Q.

But they also serve to expand horizons! We hope students will acquire a handson feeling for the various basis fimctions already discussed in the book; and more importantly, get started at building bases of his/her own. , [Hal67]. , [Dav96]. Finally, several of our exercises have been put in to expand on themes inside the text, pointing the reader to new developments in the subject, and especially stressing links to neighboring subjects and to applications; pointing to connections between modem trends and classical subjects, highlighting an especially powerfiil (and beautifiil) idea, or even suggesting unorthodox applications.

1) are called masking coefficients, filters, or filter coefficients. For special values of the coefficients, it turns out that there is a normalized Z^ solution cp, and that pointwise convergence of a good approximation can be established in a meaningfiil way. , or Ruelle operator. 1) is also called a subdivision because of the function values (p{Nt — A:). 1) on some initial fimction is called a cascade approximation. 5) for the Fourier transform of ^. The relation between cp and its scaled refinement is well understood when we pass from the time domain to the frequency domain via the Fourier transform.

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