The construction of boundary filters without DC leakage for two-channel paraunitary FIR filter banks is considered. The design procedure is based on orthogonal boundary filters which are optimal in a weighted mean square error sense in the Fourier domain and on Householder transformation of boundary filter matrices. Simulation results are presented for boundary filters based on minimum-phase Da...

Let P be an r×smatrix of Laurent polynomials with symmetry such that P(z)P∗(z) = Ir for all z ∈ C\{0} and the symmetry of P is compatible. The matrix extension problem with symmetry is to find an s × s square matrix Pe of Laurent polynomials with symmetry such that [Ir,0]Pe = P (that is, the submatrix of the first r rows of Pe is the given matrix P), Pe is paraunitary satisfying Pe(z)Pe(z) = Is...

Periodic or symmetric extensions are commonly used for processing images and other finitelength signals with a paraunitary Alter bank (PUFB). Unlike infinite-length signals, PUFBs applied to finite-length signals will not necessarily lead to an orthogonal system. We show that for symmetric extensions, orthogonality is only possible for special PUFBs based on linearphase Alters. We also discuss ...