Singular value decomposition for comb filter matrices

In this paper, we present an eigenvalue decomposition for any n×nn×n complex matrix with constant diagonals Tn=(aj-k)j,k=1n satisfying that there exists a positive integer m   such that ak=0ak=0 for all k∉{-m,0,m}. Moreover, from this eigenvalue decomposition we obtain a singular value decomposition for any comb filter matrix.