TY - JOUR
T1 - Orthogonal polynomial wavelets
AU - Fischer, Bernd
AU - Themistoclakis, Woula
PY - 2002/12/1
Y1 - 2002/12/1
N2 - Recently Fischer and Prestin presented a unified approach for the construction of polynomial wavelets. In particular, they characterized those parameter sets which lead to orthogonal scaling functions. Here, we extend their results to the wavelets. We work out necessary and sufficient conditions for the wavelets to be orthogonal to each other. Furthermore, we show how these computable characterizations lead to attractive decomposition and reconstruction schemes. The paper concludes with a study of the special case of Bernstein-Szegö weight functions.
AB - Recently Fischer and Prestin presented a unified approach for the construction of polynomial wavelets. In particular, they characterized those parameter sets which lead to orthogonal scaling functions. Here, we extend their results to the wavelets. We work out necessary and sufficient conditions for the wavelets to be orthogonal to each other. Furthermore, we show how these computable characterizations lead to attractive decomposition and reconstruction schemes. The paper concludes with a study of the special case of Bernstein-Szegö weight functions.
UR - http://www.scopus.com/inward/record.url?scp=0036274207&partnerID=8YFLogxK
U2 - 10.1023/A:1015689418605
DO - 10.1023/A:1015689418605
M3 - Journal articles
AN - SCOPUS:0036274207
SN - 1017-1398
VL - 30
SP - 37
EP - 58
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 1
ER -