Multiwavelets are generated from refinable function vectors by using multiresolution analysis. In this paper we investigate the approximation properties of a multivariate refinable function vector associated with a general dilation matrix in terms of both the subdivision operator and the order of sum rules satisfied by the matrix refinement mask. Based on a fact about the sum rules of biorthogo...

The vertical or horizontal edges don’t dominate in some frames of video sequence, so the conventional discrete cosine transform (DCT) may not be the best choice for those frames. Directional DCT framework behaves better than conventional DCT in coding performance for images where directional edges dominate. In addition, the all phase biorthogonal transform (APBT), which is used in image compres...

In this paper, we propose and analyze a multiuser receiver using a decorrelating filter and Viterbi decoders for trellis-coded direct-sequence code-division multiple-access (DS/CDMA) systems with biorthogonal signal constellation in asynchronous channels. The biorthogonality is implemented by user signature waveforms and the decorrelating filter. The performance of the proposed system is invest...

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.

In this paper, the existence, regularity and biorthogonality of the solution of the nonhomogeneous reenement equation (x) = X k2Z Z d 0 c k (2x ? k) + G(x); x 2 IR d are considered. Also new class of biorthogonal wavelet basis on a non-uniform grid is constructed.

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...

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