By Topic

Wavelets with convolution-type orthogonality conditions

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
K. Niijima ; Dept. of Inf., Kyushu Univ., Fukuoka, Japan ; K. Kuzume

Wavelets with free parameters are constructed using a convolution-type orthogonality condition. First, finer and coarser scaling function spaces are introduced with the help of a two-scale relation for scaling functions. An inner product and a norm having convolution parameters are defined in the finer scaling function space, which becomes a Hilbert space as a result. The finer scaling function space can be decomposed into the coarser one and its orthogonal complement. A wavelet function is constructed as a mother function whose shifted functions form an orthonormal basis in the complement space. Such wavelet functions contain the Daubechies' compactly supported wavelets as a special case. In some restricted cases, several symmetric and almost compactly supported wavelets are constructed analytically by tuning free convolution parameters contained in the wavelet functions

Published in:

IEEE Transactions on Signal Processing  (Volume:47 ,  Issue: 2 )