Constructions of Vector-Valued Filters and Vector-Valued Wavelets

Abstract EN

Let a =(a1,a2,…,am)∈ℂm be an m-dimensional vector.

Then, it can be identified with an m×m circulant matrix.

By using the theory of matrix-valued wavelet analysis (Walden and Serroukh, 2002), we discuss the vector-valued multiresolution analysis.

Also, we derive several different designs of finite length of vector-valued filters.

The corresponding scaling functions and wavelet functions are given.

Specially, we deal with the construction of filters on symmetric matrix-valued functions space.