Interpolatory and Orthonormal Trigonometric Wavelets

Abstract. The aim of this paper is the detailed investigation of trigonometric polynomial spaces as a tool for approximation and signal analysis. Sample spaces are generated by equidistant translates of certain de la Vallee Poussin means. The different de la Vallee Poussin means enable us to choose between better time or frequency localization. For nested sample spaces and corresponding wavelet spaces, we discuss different bases and their transformations.

[1]  A. Timan.  Theory of Approximation of Functions of a Real Variable , 1994 .

[2]  Przemysław Wojtaszczyk,et al.  Orthonormal polynomial bases in function spaces , 1991 .

[3]  C. Chui,et al.  Wavelets : theory, algorithms, and applications , 1994 .

[4]  Y. Meyer,et al.  Ondelettes et bases hilbertiennes. , 1986 .

[5]  Jürgen Prestin.  On the approximation by de la Vallée Poussin sums and interpolatory polynomials in Lipschitz norms , 1987 .

[6]  J. David Brown,et al.  Proceedings of the Cornelius Lanczos International Centenary Conference , 1994 .

[7]  Kathi Selig,et al.  Trigonometric Wavelets for Time-Frequency-Analysis , 1995 .

[8]  R. A. Lorentz,et al.  Orthogonal Trigonometric Schauder Bases of Optimal Degree for C(K) , 1994 .

[9]  ON AN ORTHOGONAL TRIGONOMETRIC BASIS , 1992 .

[10]  Gerlind Plonka-Hoch,et al.  On the construction of wavelets on a bounded interval , 1995, Adv. Comput. Math..

[11]  P. Heywood.  Trigonometric Series , 1968, Nature.

[12]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[13]  Manfred Tasche.  Polynomial Wavelets on [-1, 1] , 1995 .

[14]  Manfred Tasche,et al.  A Unified Approach to Periodic Wavelets , 1994 .

[15]  Jürgen Prestin,et al.  Polynomial wavelets on the interval , 1996 .

[16]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[17]  D. Offin,et al.  A note on orthonormal polynomial bases and wavelets , 1993 .

[18]  A duality principle for trigonometric wavelets , 1994 .

[19]  H. Mhaskar,et al.  On trigonometric wavelets , 1993 .

[20]  Larry L. Schumaker,et al.  Wavelets, Images, and Surface Fitting , 1994 .

[21]  Sankatha Prasad Singh,et al.  Approximation Theory, Wavelets and Applications , 1995 .