A new implementation of the critically sampled nonperiodic real Gabor transform (GT) is presented for non-separable time-frequency (TF) plane sampling. In the propsed implementation, the quincunx sampling is used to sample the TF plane. This leads to a well localized biorthogonal function in both time and frequency. It thus overcomes the main problem of the previous implementations, which is th...

We give a formula for the duals of the masks associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.

In this paper, we describe an algorithm for computing biorthogonal compactly supported dyadic wavelets related to the Walsh functions on the positive half-line R+. It is noted that a similar technique can be applied in very general situations, e.g., in the case of Cantor and Vilenkin groups. Using the feedback-based approach, some numerical experiments comparing orthogonal and biorthogonal dyad...

Over the last number of years many different libraries of biorthogonal wavelets have been designed. In addition, the lifting scheme has been developed which unifies the design of biorthogonal wavelets using a simple approach. The lifting scheme allows the custom design of wavelets while maintaining the biorthogonal constraint on the filter bank. A drawback of the lifting scheme is that it does ...

In this paper we study the algebraic and geometric structure of the space of compactly supported biorthogonal wavelets. We prove that any biorthogonal wavelet matrix pair (which consists of the scaling lters and wavelet lters) can be factored as the product of primitive parau-nitary matrices, a pseudo identity matrix pair, an invertible matrix, and the canonical Haar matrix. Compared with the f...

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...

In this correspondence, we generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M -channel. A sufficient condition for the M -channel perfect reconstruction filter banks to constructM -channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal M -channel wavelet bases is equivalent to the design of a...

In this paper, we shall discuss how to construct multidimensional biorthogonal wavelets by employing a coset by coset (CBC) algorithm. We shall construct biorthogonal wavelets on the hexagonal lattice by CBC algorithm. In particular, we shall propose a CBC algorithm to construct inter-polatory biorthogonal wavelets which are derived from pairs of fundamental reenable functions. More precisely, ...