we present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -11 & 1 & 0 1 &  0 & 1end{array}right )$-wavelets  under a mild condition. wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. as an application, an  example is  provided.

We introduce ternary wavelets, based on an interpolating 4-point C ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). H...

we consider an approximation scheme using haar wavelets for solving a class of infinite horizon optimal control problems (ocp's) of nonlinear interconnected large-scale dynamic systems. a computational method based on haar wavelets in the time-domain is proposed for solving the optimal control problem. haar wavelets integral operational matrix and direct collocation method are utilized to ...

In this work, wavelets are used in the analysis of medical images, where efficiency mathematics field has been proven because basis proposed work is newly constructed mathematical equations, and through MATLAB program, many programs have designed to be ready for use image study. Physical samples were selected that compressed using wavelets, good results obtained prove method used.

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector lter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued ...

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

In many applications, including analysis of seismic signals, Daubechies wavelets perform much better than other families wavelets. this paper, we provide a possible theoretical explanation for the empirical success Specifically, show that these are optimal with respect to any optimality criterion satisfies natural properties scale- and shift-invariance.

A new class of biorthogonal wavelets—interpolating distributed approximating functional (DAF) wavelets are proposed as a powerful basis for scale-space functional analysis and approximation. The important advantage is that these wavelets can be designed with infinite smoothness in both time and frequency spaces, and have as well symmetric interpolating characteristics. Boundary adaptive wavelet...

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated to Legendre multiresolution analysis is ...