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Efficient wavelet prefilters with optimal time-shifts
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.ORCID-id: 0000-0001-7620-9386
2005 (engelsk)Inngår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, nr 7, s. 2451-2461Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

A wavelet prefilter maps sample values of an analyzed signal to the scaling function coefficient input of standard discrete wavelet transform (DWT) algorithms. The prefilter is the inverse of a certain postfilter convolution matrix consisting of integer sample values of a noninteger-shifted wavelet scaling function. For the prefilter and the DWT algorithms to have similar computational complexity, it is often necessary to use a "short enough" approximation of the prefilter. In addition to well-known quadrature formula and identity matrix prefilter approximations, we propose a Neumann series approximation, which is a band matrix truncation of the optimal prefilter, and derive simple formulas for the operator norm approximation error. This error shows a dramatic dependence on how the postfilter noninteger shift is chosen. We explain the meaning of this shift in practical applications, describe how to choose it, and plot optimally shifted prefilter approximation errors for 95 different Daubechies, Symlet, and B-spline wavelets. Whereas the truncated inverse is overall superior, the Neumann filters are by far the easiest ones to compute, and for some short support wavelets, they also give the smallest approximation error. For example, for Daubechies 1-5 wavelets, the simplest Neumann prefilter provide an approximation error reduction corresponding to 100-10 000 times oversampling in a nonprefiltered system.

sted, utgiver, år, opplag, sider
2005. Vol. 53, nr 7, s. 2451-2461
HSV kategori
Forskningsprogram
Matematik
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URN: urn:nbn:se:ltu:diva-13797DOI: 10.1109/TSP.2005.849188ISI: 000230216800017Scopus ID: 2-s2.0-23844494743Lokal ID: d1722700-a544-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-13797DiVA, id: diva2:986750
Merknad
Validerad; 2005; 20070116 (evan)Tilgjengelig fra: 2016-09-29 Laget: 2016-09-29 Sist oppdatert: 2018-07-10bibliografisk kontrollert

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