On Sampling Theorem For Multiwavelet Subspaces And Generalized Cardinal Multiwavelets

A general sampling theorem for multiwavelet subspaces is introduced by using Zak transform.At present..the sampling theorem for tnultiwavelet subspaces given hy [22] reconstructing a signal perfectly and completing A/D and D/A exactly~ While his sampling theorem in mnltiresolution spaces with scaling functions as interpolant.s is just the special case of our results.Moreover. his multiwavelets have required the solution of large system of nonlinear equation and can抰 have symmetry property except for orthogonalitv.short-compact support.high appromation order.halanced propertv,etc. which is disadvantaged to signal processing,especially,irnage compressing.hi this paper. the emphasis of our theorems are on a large family of multiwavelets with good properties including symmetry(GHM抯 mnlt.iwavelet. is a case and completes t.he exact. A,/D and D/A,t.oo). In addition.we devote to a study of general cardinal rnultiwavelet svstem~based on a signal in the mult.iresolutiou space V0Q~) can be perfectly reconstructed by integer and semiinteger uniform shift sampling in the case of the multiscaLing function with general cardinal propert.y.In this case.t.he exact. A/D and D,/A can be compelet. So we investigate the relationship among interpolating propertv.orthogonalitv.shortcompact. and symmetry and mainly present and prove the necessity and sufficiencv of the conditions hot.h of general cardinal orthogonal multiwavelets and general cardinal symmetrical multiwavelets.The examples of the general cardinal multiwavelet,s with some good properties are given by Hopfield feedback neural networks instead of t.he software Sin gii.Iar.It. not. only significantly get.s over the time梒ost. by sin 9uI(Jr carrying out the G b bnFr 1)aSis cornpiit.atioiis.hnt. also obtain the satisfied solutions when the proper initial values are chosen.