52 research outputs found
Symmetric interpolatory dual wavelet frames
For any symmetry group and any appropriate matrix dilation we give an
explicit method for the construction of -symmetric refinable interpolatory
refinable masks which satisfy sum rule of arbitrary order . For each such
mask we give an explicit technique for the construction of dual wavelet frames
such that the corresponding wavelet masks are mutually symmetric and have the
vanishing moments up to the order n. For an abelian symmetry group we
modify the technique such that each constructed wavelet mask is -symmetric.Comment: 22 page
A New Family of PR Two Channel Filter Banks
A new family of multidimensional dimensional (MD) perfect reconstruction (PR) two channel filter banks with finite impulse response (FIR) filters induced from systems of biorthogonal MD scaling functions and wavelets are introduced. One of the advantages of this construction is that the biorthogonal scaling functions and wavelets are easy to establish due to the interpolatory property of the scaling functions to start with. The other advantage is that all filters can be centrosymmetric or bi-linear phase. Examples of two dimensional (2D) bi-linear phase PR twochannel FIR filter banks will be demonstrated
Bidimensional PR QMF with FIR Filters
Multidimensional perfect reconstruction (PR) quadrature mirror filter (QMF) banks with finite impulse response (FIR) filters induced from systems of biorthogonal multivariate scaling functions and wavelets are investigated. In particular, bivariate scaling functions and wavelets with dilation as an expansive integer matrix whose determinant is two in absolute value are considered. Demonstrative quincunxial examples are explicitly given and new FIR filters are constructed
Pairs of Frequency-based Nonhomogeneous Dual Wavelet Frames in the Distribution Space
In this paper, we study nonhomogeneous wavelet systems which have close
relations to the fast wavelet transform and homogeneous wavelet systems. We
introduce and characterize a pair of frequency-based nonhomogeneous dual
wavelet frames in the distribution space; the proposed notion enables us to
completely separate the perfect reconstruction property of a wavelet system
from its stability property in function spaces. The results in this paper lead
to a natural explanation for the oblique extension principle, which has been
widely used to construct dual wavelet frames from refinable functions, without
any a priori condition on the generating wavelet functions and refinable
functions. A nonhomogeneous wavelet system, which is not necessarily derived
from refinable functions via a multiresolution analysis, not only has a natural
multiresolution-like structure that is closely linked to the fast wavelet
transform, but also plays a basic role in understanding many aspects of wavelet
theory. To illustrate the flexibility and generality of the approach in this
paper, we further extend our results to nonstationary wavelets with real
dilation factors and to nonstationary wavelet filter banks having the perfect
reconstruction property
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