This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing err...This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing error. the setting of a class of bidimensional matrix of determinant ±2. The explicit is established, from which we obtain an展开更多
It is focused on the orthogonal M-band wavelet approximation power for band-limited signals and on the quantitative analysis of the approximation behavior of scaling filters and scaling function frequency response nea...It is focused on the orthogonal M-band wavelet approximation power for band-limited signals and on the quantitative analysis of the approximation behavior of scaling filters and scaling function frequency response near zero. A sharp upper bound of the approximation errors in multiresolution subspaces is obtained for band-limited signals. With this bound one may select better wavelet base and corresponding smaller scale factor to satisfy the given measure of the approximation error. Finally, the experiments of 2-band Daubechies wavelet bases show that signals with the normalized energy and bandwidth almost belong to \%V\-2\% spanned by \%D\%\-8 with the satisfactory error measure.展开更多
基金Supported by the National Natural Science Foundation of China (10671008)Beijing Natural Science Foundation (1092001)+2 种基金the Scientific Research Common Program of Beijing Municipal Commission of Educationthe Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry (SRF for ROCS, SEM)
文摘This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing error. the setting of a class of bidimensional matrix of determinant ±2. The explicit is established, from which we obtain an
文摘It is focused on the orthogonal M-band wavelet approximation power for band-limited signals and on the quantitative analysis of the approximation behavior of scaling filters and scaling function frequency response near zero. A sharp upper bound of the approximation errors in multiresolution subspaces is obtained for band-limited signals. With this bound one may select better wavelet base and corresponding smaller scale factor to satisfy the given measure of the approximation error. Finally, the experiments of 2-band Daubechies wavelet bases show that signals with the normalized energy and bandwidth almost belong to \%V\-2\% spanned by \%D\%\-8 with the satisfactory error measure.
