Mallet, Y., De Vel, O., and Coomans, D. (2000) The discrete wavelet transform in practice. In: Walczak, Beata, (ed.) Wavelets in Chemistry. Data Handling in Science and Technology (22). Elsevier, Amsterdam, The Netherlands, pp. 85-118.

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Abstract

In this chapter we present the finite discrete wavelet transform (DWT) using matrices. The main difference between the description of the DWT in this chapter, compared to the description given in the previous chapter, is now we consider the DWT for discrete data, as opposed to continuous functions. We first provide a brief introduction to matrix theory and discuss some special forms of matrices such as, orthogonal and banded matrices. We then give the matrix representation of the DWT for finite-length signals and discuss some of the practical issues, including signal length and boundary conditions. The same techniques presented in this chapter can be extended to provide the basis for the development of task specific wavelets in Chapter 7. The reader who is familiar with matrix terms and definitions may skip Section 2.

Item ID:	39875
Item Type:	Book Chapter (Research - B1)
ISBN:	978-0-444-50111-0
Date Deposited:	18 Aug 2015 02:17
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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