We present new multiwavelet transforms for discrete signals. The transforms are implemented in two phases: 1. Pre (post)processing which transform the scalar signal into the vector one (and back). 2.Wavelet transforms of the vector signal. Both phases are performed in a lifting manner. We use the cubic interpolatory Hermite splines as a predicting aggregate in the vector wavelet transform. We p...

Orthogonal, semiorthogonal and biorthogonal wavelet bases are special cases of oblique multiwavelet bases. One of the advantage of oblique multiwavelets is the flexibility they provide for constructing bases with certain desired shapes and/or properties. The decomposition of a signal in terms of oblique wavelet bases is still a perfect reconstruction filter bank. In this paper, we present sever...

Orthogonal frequency division multiplexing (OFDM) is a popular modulation technique that is widely utilized in many wireless communication systems. Traditional OFDM based on fast Fourier transform (FFT) involves the use of a rectangular window; consequently, high side lobes are created. Hence, OFDM based on discrete multiwavelet critical sampling transform (DMWTCS) is proposed in this paper. DM...

This paper describes the first steps toward a multiwavelet system that may retain the advantages of a traditional multiwavelet system while alleviating some of its disadvantages. We attempt to achieve this through the introduction of a novel property — the disjoint support of the multiscaling functions. We derive the conditions on the matrix filter coefficients that guarantee the disjoint suppo...

In this paper we construct IR n-valued biorthogonal, compactly supported multiwavelet families such that one of the biorthogo-nal pairs consists of divergence-free vector wavelets. The construction is based largely on Lemari e's idea of multiresolution analyses intertwined by diierentiation. We show that this technique extends nontrivially to multiwavelets via Strela's two-scale transform. An e...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...

Multiwavelet transform has received attention in image watermarking because it is possible to construct multiwavelets that simultaneously possess desirable properties. Since the choice of appropriate multiwavelet basis is a critical issue that affects the quality of the watermarked image and the robustness of the watermark, we selected five different multiwavelet bases in this paper to evaluate...

In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...

This paper investigates the emerging notion of multiwavelets in the context of multirate filter banks, and applies a multiwavelet system to image coding. Multiwavelets are of interest because their constituent filters can be simultaneously symmetric and orthogonal (this combination is impossible for 2-band PR-QMFs), and because one can obtain higher orders of approximation (more vanishing wavel...