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Abstract: In this paper we propose a procedure which allows the construction of a large family of FIR matrix wavelet filters by exploiting the one-to-one correspondence between QMF systems and orthogonal operators which commute with the shifts by two. A characterization of the class of filters of full rank type that can be obtained with such procedure is given. In particular, we restrict our attention to a special construction based on the representation of in terms of the elements of its Lie algebra. Explicit expressions for the filters in the case are given, as a result of a local analysis of the parameterization obtained from perturbing the Haar system. [Copyright &y& Elsevier]

Abstract: In this work, we present a computational method for solving nonlinear Fredholm integral equations of the second kind which is based on the use of Haar wavelets. Error analysis is worked out that shows efficiency of the method. Finally, we also give some numerical examples. [Copyright &y& Elsevier]

Abstract: In this paper, an algorithm for computing the Hilbert transform based on the Haar multiresolution approximation is proposed and the -error is estimated. Experimental results show that it outperforms the library function ‘hilbert’ in Matlab (The MathWorks, Inc. 1994–2007). Finally it is applied to compute the instantaneous phase of signals approximately and is compared with three existing methods. [Copyright &y& Elsevier]