Let P be the transform group on R n, then P has a natural unitary representation U on L 2(R n). Decompose L 2(R n) into the direct sum of irreducible invariant closed subspaces. The restriction of U on ...Let P be the transform group on R n, then P has a natural unitary representation U on L 2(R n). Decompose L 2(R n) into the direct sum of irreducible invariant closed subspaces. The restriction of U on these subspaces is square integrable. In this paper the characterization of admissible condition in terms of the Fourier transform is given. The wavelet transform is defined, and the orthogonal direct sum decomposition of function space L 2(P,dμ l) ) is obtained.展开更多
In this paper, a new method of constructing symmetric (antisymmetric) scal-ing and wavelet filters is introduced, and we get a new type of wavelet system that hasvery beautiful structure. Using this kind of wavelet sy...In this paper, a new method of constructing symmetric (antisymmetric) scal-ing and wavelet filters is introduced, and we get a new type of wavelet system that hasvery beautiful structure. Using this kind of wavelet system, we can achieve filters withthe properties: rational, symmetric or antisymmetric, the lengths of the filters are shorterand the corresponding functions have higher smoothness, so they have good prospect inapplications.展开更多
文摘Let P be the transform group on R n, then P has a natural unitary representation U on L 2(R n). Decompose L 2(R n) into the direct sum of irreducible invariant closed subspaces. The restriction of U on these subspaces is square integrable. In this paper the characterization of admissible condition in terms of the Fourier transform is given. The wavelet transform is defined, and the orthogonal direct sum decomposition of function space L 2(P,dμ l) ) is obtained.
文摘In this paper, a new method of constructing symmetric (antisymmetric) scal-ing and wavelet filters is introduced, and we get a new type of wavelet system that hasvery beautiful structure. Using this kind of wavelet system, we can achieve filters withthe properties: rational, symmetric or antisymmetric, the lengths of the filters are shorterand the corresponding functions have higher smoothness, so they have good prospect inapplications.
