We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family has tension parameter ω. When ω = 0, it becomes the minimal length biorthogonal Coifman wavelet system [22]. Choosing ω away from zero, we can get better smoothness of the refinable functions at the expense of slightly larger support. Though the construction of the new ...

We construct general biorthogonal Coifman wavelet systems, a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair. A time-domain design method is employed and closed-form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived. The resulting filter ...

Conventional methods uses Fourier Transform (FT) for Bangla vowel synthesis which has resolution problem. In order to produce better accuracy, we attempted Wavelet Transform (WT) with several wavelet families for analyzing and synthesizing the seven Bangla vowels. The parameters for performance evaluation for selecting optimal wavelet for Bangla phoneme synthesis are normalized root mean square...

In this paper a biorthogonal wavelet approach based on Doo-Sabin subdivision is presented. In the dual subdivision like Doo-Sabin scheme, all the old control vertices disappear after one subdivision step, which is a big challenge to the biorthogonal wavelet construction. In our approach, the barycenters of the V-faces corresponding to the old vertices are selected as the vertices associated wit...

This paper is concerned with the construction of biorthogonal wavelet bases on n-dimensional cubes which provide Riesz bases for Sobolev and Besov spaces with homogeneous Dirichlet boundary conditions on part of the boundary. The essential point is that the primal and dual wavelets satisfy certain corresponding complementary boundary conditions. These results form the key ingredients of the con...

In this paper we investigate compactly supported wavelet bases for Sobolev spaces. Starting with a pair of compactly supported refinable functions φ and φ̃ in L2(R) satisfying a very mild condition, we provide a general principle for constructing a wavelet ψ such that the wavelets ψjk := 2j/2ψ(2j · − k) (j, k ∈ Z) form a Riesz basis for L2(R). If, in addition, φ lies in the Sobolev space H(R), t...

Let G be a countable group of unitary operators on a complex separable Hilbert space H. We give a characterization of biorthogonality among Riesz multiwavelets in terms of certain invariant properties of their associated core spaces. A large family of non-biorthogonal Riesz multiwavelets is exhibited. We also discuss some results on linear perturbation of orthonormal multiwavelets.

A contiguous relation for complementry pairs of very well poised balanced 10φ9 basic hypergeometric functions is used to derive an explict expression for the associated continued fraction. This generalizes the continued fraction results associated with both Ramanujan’s Entry 40 and Askey-Wilson polynomials which can be recovered as limits. Associated with our continued fraction results there ar...

We give a general approach to in nite dimensional non-Gaussian analysis which generalizes the work [KSWY95]. For given measure we construct a family of biorthogonal systems. We study their properties and their Gel'fand triples that they generate. As an example we consider the measures of Poisson type.

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