Wavelet packet transforms and best basis algorithms

The wavelet packet transform (WPT) [1] is an extension of the discrete wavelet transform (DWT). The basic difference between the wavelet packet transform and the wavelet transform relates to which coefficients are passed through the low-pass and high-pass filters. With the wavelet transform, the scaling coefficients are filtered through each of these filters. With the WPT, not only do the scaling coefficients pass through the low-pass and high-pass filters, but so do the wavelet coefficients. Since both the scaling and wavelet coefficients are filtered there is a surplus of information stored in the WPT which has a binary tree structure. An advantage of this redundant information is that it provides greater freedom in choosing an orthogonal basis. The best basis algorithm [2] seeks a basis in the WPT which optimizes some criterion function. Thus, the best basis algorithm is a task specific algorithm in that the particular basis is dependent upon the role for which it will be used.

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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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