Smooth multiwavelets based on two scaling functions

In this paper new multiwavelets based on several scaling functions are designed. The resulting wavelets exhibit the following properties: compact support, symmetry and orthogonality, arbitrary approximation order as well as good frequency resolution. The new bases are quite similar to the well known splines and also have close relationships to multirate filterbanks (multiwavelets based on one scaling function). The good performance of the new wavelets with respect to the smoothness and the frequency resolution is documented. A filterbank implementation is discussed.

[1]  D. Hardin,et al.  Fractal Functions and Wavelet Expansions Based on Several Scaling Functions , 1994 .

[2]  Truong Q. Nguyen,et al.  Linear phase paraunitary filter banks: theory, factorizations and designs , 1993, IEEE Trans. Signal Process..

[3]  J. Gotze,et al.  Multiwavelet transforms based on several scaling functions , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[4]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[5]  Gilbert Strang,et al.  Short wavelets and matrix dilation equations , 1995, IEEE Trans. Signal Process..

[6]  Josef A. Nossek,et al.  Algebraic design of discrete multiwavelet transforms , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[7]  Gilbert Strang,et al.  Finite element multiwavelets , 1994, Optics & Photonics.

[8]  Xiang-Gen Xia,et al.  Computations of multiwavelet transforms , 1995, Optics + Photonics.

[9]  Truong Q. Nguyen,et al.  Linear-phase M-band wavelets with application to image coding , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[10]  Michel Barlaud,et al.  Image coding using wavelet transform , 1992, IEEE Trans. Image Process..