Matrix methods of constructing wavelet filters and discrete hyper-wavelet transforms
Guoqiu Wang · Optical Engineering · 2000
Guoqiu WangHunan Normal UniversityDepartment of Mathematics and ComputerScienceChangsha, Hunan 410006ChinaE-mail: [email protected]. The Mallat algorithm for finite length signals is equivalent to amatrix transform on vector space, and the transform matrix is a finite2-circular matrix. As a new concept, a minimal matrix, which is also a2-circular matrix, is put forward. Through new developments of defini-tions and theorems for a minimal matrix, new algorithms for constructingwavelets filters are obtained. Employing these algorithms, we give sev-eral examples of orthonormal and biorthogonal wavelet filters. The meth-ods avoid using a Z-transform or Fourier transform, so it is relativelysimple to construct FIR wavelet filters. Because many filters constructedgo beyond traditional wavelets, the new concept of discrete hyper-wavelets transforms is put forward. Finally, an application in image com-pression is discussed briefly.