Approximate eigenvalue decomposition of para-Hermitian systems through successive FIR paraunitary transformations

The eigenvalue decomposition (EVD) of a Hermitian matrix in terms of unitary matrices is well known. In this paper, we present an algorithm for the approximate EVD (AEVD) of a para-Hermitian (PH) system. Here, the approximate diagonalization is carried out successively by applying degree-1 finite impulse response (FIR) paraunitary (PU) transformations. The system parameters are chosen to make the zeroth order diagonal energy (ZODE) nondecreasing at each stage. Simulation results presented for the design of a signal-adapted PU filter bank (FB) show close agreement with the behavior of the infinite order principal component FB (PCFB).