Fundamentals of wavelet transformations

Mallet, Y., De Vel, O., and Coomans, D. (2000) Fundamentals of wavelet transformations. In: Walczak, Beata, (ed.) Wavelets in Chemistry. Data Handling in Science and Technology (22). Elsevier, Amsterdam, The Netherlands, pp. 57-84.

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This chapter discusses various aspects of the wavelet transform when applied to continuous functions or signals. It may seem strange why this book has a chapter dealing with wavelet analysis for continuous functions, since, in practice most of us will be dealing with discretised functions or discrete signals. Here we think of a discrete signal being equivalent to a discrete near infrared spectrum, for example. Whilst continuous functions are not practical, they do assist substantially, in providing an understanding of the basic concepts and theories associated with wavelet analysis. A link actually emerges between wavelet transforms for continuous functions and discrete signals. Before we embark on a discussion on the fundamentals of wavelet transforms associated with continuous functions, we diverge momentarily to present a simple example and to provide motivation for the use of wavelet methods in signal analysis. This example does not use a continuous function, rather a sine curve which has been sampled 512 times.

Item ID: 39873
Item Type: Book Chapter (Research - B1)
ISBN: 978-0-444-50111-0
Date Deposited: 17 Aug 2015 23:34
FoR Codes: 01 MATHEMATICAL SCIENCES > 0104 Statistics > 010401 Applied Statistics @ 100%
SEO Codes: 96 ENVIRONMENT > 9699 Other Environment > 969999 Environment not elsewhere classified @ 100%
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