DocumentCode :
1410067
Title :
A framework for multiscale and hybrid RKHS-based approximators
Author :
Van Wyk, Michael A. ; Durrani, Tariq S.
Author_Institution :
Dept. of Electr. & Electron. Eng., Rand Afrikaans Univ., Johannesburg, South Africa
Volume :
48
Issue :
12
fYear :
2000
fDate :
12/1/2000 12:00:00 AM
Firstpage :
3559
Lastpage :
3568
Abstract :
A generalized framework for deriving multiscale and hybrid functionally expanded approximators that are linear in the adjustable weights is presented. The basic idea here is to define one or more appropriate function spaces and then to impose a geometric structure on these to obtain reproducing kernel Hilbert spaces (RKHSs). The weight identification problem is formulated as a minimum norm optimization problem that produces an approximation network structure that comprises a linear weighted sum of displaced reproducing kernels fed by the input signals. Examples of the application of this framework are discussed. Results of numerical experiments are presented.
Keywords :
Hilbert spaces; function approximation; identification; interpolation; optimisation; signal processing; time series; Shannon interpolator; adjustable weights; approximation network structure; displaced reproducing kernels; experimental time series; functionally expanded approximator; geometric structure; hybrid RKHS-based approximator; input signals; linear weighted sum; low computational complexity; minimum norm optimization problem; multiscale RKHS-based approximator; multiscale Shannon interpolator; numerical experiments; reproducing kernel Hilbert spaces; weight identification; Differential equations; Hilbert space; Integral equations; Kernel; Linear approximation; Neural networks; Partial differential equations; Signal processing; Signal processing algorithms; Transforms;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.887048
Filename :
887048
Link To Document :
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