Construcción de wavelets splines sobre intervalos acotados
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Date
2024
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Universidad Nacional de Trujillo
Abstract
En este trabajo de investigación se determinó una base de wavelets splines sobre intervalos acotados de la forma [0, r], con r ∈ N. El primero en construir wavelets sobre intervalos acotados fue Meyer que restringió las funciones de escalamiento de Daubechie a [0, 1]. El enfoque presentado en este trabajo se basa en las wavelets splines de Chui-Wang y hace uso del concepto de nudos múltiples para construir funciones de escalamiento y wavelets de frontera. Por último, se presentan algoritmos wavelets de descomposición y reconstrucción sobre intervalos acotados que permiten determinar los coeficientes wavelets asociados a la base wavelet spline establecida.
Abstract In this research work a base of wavelet splines on bounded intervals of the form [0, r] was determined, with r ∈ N. The first to build wavelets on bounded intervals was Meyer who restricted the Daubechie scaling functions to [0, 1]. The approach presented in this work is based on the Chui-Wang wavelet splines and makes use of the concept of multiple nodes to construct scaling functions and boundary wavelets. Finally, wavelet decomposition and reconstruction algorithms on bounded intervals are presented that allow determining the wavelet coefficients associated with the established wavelet spline basis
Abstract In this research work a base of wavelet splines on bounded intervals of the form [0, r] was determined, with r ∈ N. The first to build wavelets on bounded intervals was Meyer who restricted the Daubechie scaling functions to [0, 1]. The approach presented in this work is based on the Chui-Wang wavelet splines and makes use of the concept of multiple nodes to construct scaling functions and boundary wavelets. Finally, wavelet decomposition and reconstruction algorithms on bounded intervals are presented that allow determining the wavelet coefficients associated with the established wavelet spline basis
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Keywords
Wavelets splines, análisis multiresolución, intervalos acotados, función de
escalamiento