Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers (1994)
Pacific Grove, CA, USA
Oct. 31, 1994 to Nov. 2, 1994
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
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.<
signal resolution, spectral analysis, least squares approximations, recursive estimation, wavelet transforms, minimisation
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.