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- Kathi Selig
- 1995

The time-frequency localization of trigonometric wavelets is discussed. A good measure is provided by a periodic version of the Heisenberg uncertainty principle. We consider multiresolution analyses generated by de la Vall ee Poussin means of the Dirichlet kernel. For the resulting interpolatory and orthonormal scaling functions and wavelets, the… (More)

A particular class of orthogonal trigonometric Schauder bases for C2 is given by periodic wavelet packet functions. These bases are of minimal growth of the polynomial degree. The focus of attention is their construction and the estimation of the Lebesgue constant. The corresponding approximation error is asymptotically optimal.

- Kathi Selig, Josh Zeevi, K. Selig
- 1998

The aim of this paper is the detailed investigation of trigono-metric polynomial spaces as a tool for approximation and signal analysis. Sample spaces are generated by equidistant translates of certain de la Vall ee Poussin means. The diierent de la Vall ee Poussin means enable us to choose between better time-or frequency-localization. For nested sample… (More)

- K. Selig
- 1995

We discuss wavelet-oriented ideas to construct bases of algebraic polynomials. In particular, the splitting in the frequency domain is extended in order to deene wavelet packets.

- Kathi Selig
- 1995

We present here a new solution for the problem of periodic time{ frequency{localized signal analysis. Working on polynomials with Fourier coeecients included in bands similar to octaves, we can vary the actual position and length of those bands and also the localization of the bases in the time domain by the choice of parameters. Having simple, fast and… (More)

- Gerlind Plonka-Hoch, Kathi Selig, Manfred Tasche
- Adv. Comput. Math.
- 1995

This paper presents a general approach to a multiresolution analysis and wavelet spaces on the interval ?1; 1]. Our method is based on the Chebyshev transform, corresponding shifts and the discrete cosine transform (DCT). For the wavelet analysis of given functions, eecient decomposition and reconstruction algorithms are proposed using fast DCT{algorithms.… (More)

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