The discrete wavelet transform in practice

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.

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Wavelets in Chemistry

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978-0-444-50111-0

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22

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