Factorizations And Construction Of Linear Phase Paraunitary Filter Banks And Higher Multiplicity Wavelets

. It is known that paraunitary matrices can be factorized into shift products of orthogonal matrices or linear factors. When number of rows of such a matrix (i. e. the number of channels of a paraunitary filter bank) is even, the symmetry constraints corresponding to linear phase property of the filter bank can be expressed as restrictions on factors---except the very first one, all must be centrosymmetric. For odd number of rows the situation is more complicated. It turns out that paraunitary matrices comprising of an even number of square blocks do not exist and quadratic centrosymmetric factors have to be used in the 0-shift product factorization. The centrosymmetric linear and quadratic factors can be easily obtained from partitions of centrosymmetric orthogonal matrices. Their parameterizations are also described. The characterizations of paraunitary matrices obtained from these factorizations are complete; the question of number of free parameters is discussed. Furthermore, the p..