The Stromberg wavelet and the Franklin system

Author

Kateb, Djalil ; Drouiche, Karim

Author_Institution

Dept. Statistiques, Univ. de Paris-Sud, Orsay, France

Volume

41

Issue

12

fYear

1993

fDate

12/1/1993 12:00:00 AM

Firstpage

3562

Lastpage

3566

Abstract

The Franklin (1928) system is an orthonormal basis of L²[0, 1]. The authors give a multiresolution analysis of L ²[0, 1] and study the reconstruction error made when the Stromberg (see Proc. 21 Nordic Conf. Math., June 1992) analysis (on [0, 1]) is performed instead of the Franklin one. They derive a fast algorithm which enables one to analyze and synthesize a given signal on an interval. Special considerations are held near the edges where the extension of the interval is no longer needed (zero-padding method, etc.). Numerical simulations are provided to emphasize the performances of their results

Keywords

error analysis; signal processing; signal synthesis; wavelet transforms; Franklin system; Stromberg analysis; Stromberg wavelet; fast algorithm; multiresolution analysis; numerical simulations; orthonormal basis; reconstruction error; zero-padding method; 1f noise; Discrete wavelet transforms; Filters; Fractals; Gaussian noise; Maximum likelihood estimation; Motion estimation; Notice of Violation; Signal processing algorithms; Signal resolution;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.258097

Filename

258097