On the construction of wavelets on a bounded interval | Zendy

Gerlind Plonka | Zendy; Kathi Selig | Zendy; Manfred Tasche | Zendy

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On the construction of wavelets on a bounded interval

Author(s) -

Gerlind Plonka,

Kathi Selig,

Manfred Tasche

Publication year - 1995

Publication title -

advances in computational mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.003

H-Index - 61

eISSN - 1572-9044

pISSN - 1019-7168

DOI - 10.1007/bf02123481

Subject(s) - wavelet , discrete cosine transform , mathematics , multiresolution analysis , transformation (genetics) , interval (graph theory) , bounded function , chebyshev filter , chebyshev polynomials , trigonometric functions , algorithm , scaling , discrete wavelet transform , mathematical analysis , wavelet transform , computer science , artificial intelligence , combinatorics , geometry , image (mathematics) , biochemistry , chemistry , gene

International audienceThis paper presents a general approach to a multi resolution analysis and wavelet spaces on the interval $[-1, 1]$. Our method is based on the Chebyshev transform, corresponding shifts and the discrete cosine transformation (DCT). For the wavelet analysis of given functions, efficient decomposition and reconstruction algorithms are proposed using fast DCT-algorithms. As examples for scaling functions and wavelets, polynomials and transformed splines are considered

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