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Daubechies wavelet filter computation



W = dbaux(N,SUMW) is the order N Daubechies scaling filter such that sum(W) = SUMW. Possible values for N are 1, 2, 3, ...

W = dbaux(N) is equivalent to W = dbaux(N,1)

W = dbaux(N,0) is equivalent to W = dbaux(N,1)



The algorithm used is based on a result obtained by Shensa (see "References"), showing a correspondence between the "Lagrange à trous" filters and the convolutional squares of the Daubechies wavelet filters.

The computation of the order N Daubechies scaling filter w proceeds in two steps: compute a "Lagrange à trous" filter P, and extract a square root. More precisely:

Note that other methods can be used; see various solutions of the spectral factorization problem in Strang-Nguyen (p. 157).


The computation of the dbN Daubechies scaling filter requires the extraction of the roots of a polynomial of order 4N. Instability may occur when N is too large.

See Also
dbwavf, wfilters


Daubechies, I. (1992), Ten lectures on wavelets, CBMS-NSF conference series in applied mathematics, SIAM Ed.

Shensa, M.J. (1992), "The discrete wavelet transform: wedding the a trous and Mallat Algorithms," IEEE Trans. on Signal Processing, vol. 40, 10,
pp. 2464-2482.

Strang, G.; T. Nguyen (1996), Wavelets and Filter Banks, Wellesley-Cambridge Press.

  cwt dbwavf