A General Formula for the Wavelets in Fluency Approach


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.5   pp.818-824
Publication Date: 1994/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Processing and System Theory)
signals and waves,  digital signal processing,  

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Fluency approach is to deal with staircase, polygonal and band-limited signals as those in a unified series of signal spaces of which characteristics vary with the parameter of degree. Scaling functions and their duals have been obtained which fulfill a part of the requirements to constitute a multiresolutional analysis in this approach. The purpose of the present paper is to derive general formulae to express wavelets and their duals which fulfill the rest of the requirements. It is the first step to have a general expression of every possible wavelet in selecting a wavelet. The degree is limited to be arbitrary positive oddintegers so far in this paper. The genaral formulae derived in this paper are in the form of linear combinations of the sampling functions, which are scaling functions, and their duals. These formulae can be also regarded as a reduced version of the conditions for multiresolutional analysis in terms of sampling functions and their duals. The general formulae provide a start point for selecting a wavelet which decides characteristics of a multiresolutional analysis in the fluency approach. Some criteria for the concrete selection for each purpose of multiresolutional analysis and a formula for the even-degree cases are yet to be aquired in the future.