Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Publication Type
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Wavelet Decompositions For Quantitative Pattern Matching, Bruce Kessler
Wavelet Decompositions For Quantitative Pattern Matching, Bruce Kessler
Mathematics Faculty Publications
The purpose of this paper is to provide an introduction to the concepts of wavelets and multiwavelets, and explain how these tools can be used by the analyst community to find patterns in quantitative data. Three multiwavelet bases are introduced, the GHM basis from \cite{GHM}, a piecewise polynomial basis with approximation order 4 from \cite{DGH}, and a smoother approximation-order-4 basis developed by the author in previous work \cite{K}. The technique of using multiwavelets to find patterns is illustrated in a traffic-analysis example. Acknowledgements: This work supported in part by the NACMAST consortium under contract EWAGSI-07-SC-0003.
Multiwavelets For Quantitative Pattern Matching, Bruce Kessler
Multiwavelets For Quantitative Pattern Matching, Bruce Kessler
Bruce Kessler
The purpose of this paper is to provide an introduction to the concepts of wavelets and multiwavelets, and explain how these tools can be used by the analyst community to find patterns in quantitative data. Three multiwavelet bases are introduced, the GHM basis from \cite{GHM}, a piecewise polynomial basis with approximation order 4 from \cite{DGH}, and a smoother approximation-order-4 basis developed by the author in previous work \cite{K}. The technique of using multiwavelets to find patterns is illustrated in a traffic-analysis example. Acknowledgements: This work supported in part by the NACMAST consortium under contract EWAGSI-07-SC-0003.
Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements On [0,1], Bruce Kessler
Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements On [0,1], Bruce Kessler
Mathematics Faculty Publications
Geronimo, Hardin, et al have previously constructed orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on $[0,1]$. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on $[0,1]$ is insufficient for extending spline scaling vectors to scaling vectors that are both orthogonal and balanced. We are able, however, to use this technique to extend spline scaling vectors to balanced, biorthogonal scaling vectors, and we provide two large classes of this type of scaling vector, with approximation order two and three, respectively, with …