Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers (1994)

Pacific Grove, CA, USA

Oct. 31, 1994 to Nov. 2, 1994

ISSN: 1058-6393

ISBN: 0-8186-6405-3

pp: 1109-1113

J.O. Chapa , Center for Imaging Sci., Rochester Inst. of Technol., NY, USA

M.R. Raghuveer , Center for Imaging Sci., Rochester Inst. of Technol., NY, USA

ABSTRACT

This paper develops a technique for constructing an orthonormal wavelet that is optimized to a desired signal in the least squares sense, and whose associated scaling function generates an orthonormal multiresolution analysis (MRA). The key development in this paper is a recursive equation for finding the scaling function from a given wavelet, whose closed form solution gives constraints on the wavelet that guarantee an orthonormal scaling function and multiresolution analysis. The matching algorithm uses Lagrangian multipliers to minimize the mean square error between the desired and optimum wavelet power spectra.<>

INDEX TERMS

signal resolution, spectral analysis, least squares approximations, recursive estimation, wavelet transforms, minimisation

CITATION

J. Chapa and M. Raghuveer, "Constructing MRAs from desired wavelet functions,"

*Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers(ACSSC)*, Pacific Grove, CA, USA, 1995, pp. 1109-1113.

doi:10.1109/ACSSC.1994.471631

CITATIONS