The selection of filter bank in wavelet compression is crucial, affecting image quality and system design. Recently, the biorthogonal coiflet (cooklet) family of wavelet filters has been constructed [2] [4], and explicit frequency domain formulae have been developed [2] in the Bernstein polynomial basis. In this paper we use the Bernstein basis for frequency domain design and construction of bi...

Biorthogonal wavelet transform has been widely used in the fields of image denoising and image coding. It is usually realized by linear phase filters. All phase digital filter is a new type of linear phase digital filter which has been proposed in recent years and has frequency structure. On the basis of analyzing principle of biorthogonal wavelet transform and discrete cosine sequency filter (...

In many applications biorthogonal wavelets prove to be more ee-cient than orthogonal ones. In this note we present a procedure for constructing biorthogonal multi-scaling functions with any given approximation order, starting from a low pass multi-lter H 0. We show that dual low pass multi-lter F 0 can be found if det(H 0 (z)) and det(H 0 (?z)) do not have common roots. We also suggest \two-sca...

As the international video coding standard, MPEG-2 has been widely used in today’s digital video applications. However, its quantization operation is complex. To simplify this operation, we propose a new algorithm for the intra frame transform-coding in this paper, instead of the conventional algorithm that using discrete cosine transform (DCT). This new algorithm is based on the all phase bior...

Channel equalization is an important step in most applications of digital communications. In this paper we consider the equalization of Multiple Input Multiple Output (MIMO) channels. To that end we derive the theory of MIMO biorthogonal partners, a concept that has already been introduced (only in the scalar case) by the authors. We develop conditions for the existence of an FIR MIMO biorthogo...

The concept of biorthogonal partners has been introduced recently by the authors. The work presented in this paper is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers. Hence the name fractional biorthogonal partners. The conditions for the existence of stable and of FIR fractional biorthogonal partners are deriv...

In applications, it is well known that short support, high vanishing moments and reasonable smoothness are the three most important properties of a biorthogonal wavelet. Based on our previous work on analysis and construction of optimal fundamental refinable functions and optimal biorthogonal wavelets, in this paper, we shall discuss the mutual relations among these three properties. For exampl...

In applications, it is well known that short support, high vanishing moments and reasonable smoothness are the three most important properties of a biorthogonal wavelet. Based on our previous work on analysis and construction of optimal fundamental reenable functions and optimal biorthogonal wavelets, in this paper, we shall discuss the mutual relations among these three properties. For example...

where U, V are scalar functions defined on R. The model was termed the Cauchy matrix model because of the shape of the coupling term. Similarly to the case of the Hermitean one-matrix models for which the spectral statistics is expressible in terms of appropriate orthogonal polynomials [3], this two-matrix model is solvable with the help of a new family of biorthogonal polynomials named the Cau...

We use generating functions to express orthogonality relations in the form of q-beta integrals. The integrand of such a q-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegő and leads naturally to the Al-Salam-Chihara p...