The design and analysis of nearly-orthogonal symmetric wavelet filter banks has been studied. Methods for analyzing the correlation of the nearly-orthogonal filter banks are proposed. The basic idea is to impose multiple zeros at the aliasing frequency to a symmetric filter, minimize the deviation of the filter satisfying the orthogonal condition, and a nearly orthogonal filter bank can be obta...

this work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $ax = b$ and $xc = d$ with orthogonal constraint. by optimal correction approach, a general representation of the orthogonal solution is obtained. this method is tested on two examples to show that the optimal correction is eective and highly accurate.

A novel construction of compactly supported orthogonal scaling functions and wavelets with spline functions is presented in this paper. Let [Formula: see text] be the center B-spline of order n, except for the case of order one, we know [Formula: see text] is not orthogonal. But by the formula of orthonormalization procedure, we can construct an orthogonal scaling function corresponding to [For...

We give examples of problem areas in interpolation, approximation, and quadrature, that call for orthogonal polynomials not of the classical kind. We then discuss numerical methods of computing the respective Gauss-type quadrature rules and orthogonal polynomials. The basic task is to compute the coefficients in the three-term recurrence relation for the orthogonal polynomials. This can be done...

7.2.1 Orthogonal Signalling Consider the problem of communicating k bits simultaneously. In orthogonal signalling, each of the 2 combinations is encoded as a function x(t) from the family of orthogonal cosine functions. The received signal is decoded by passing it through a bank of correlators followed by thresholding the correlation value. This process can be made more robust by adding an addi...