Construction Of Vector-Valued Filters And Vector-Valued Wavelets

Let a=（a₁, a₂,···, am）∈Cmbe an m-dimensional vector. Then it can beidentified with an m×m circulant matrix. By using the theory of matrix-valuedwavelet analysis （A.T. Walden and A. Serroukh, Wavelet analysis of matrix-valuedtime-series, Proc. R. Soc. Lond. A458（2002）,157-179）, we discuss the vector-valued multi-resolution analysis. Also, we derive several different designs of finitelength of vector-valued filters. The corresponding scale function and wavelet functionare given. Specially, we deal with the construction of filters on symmetric matrix-valued function space.