Design of 2-D Linear Phase Digital Filters Using Schur Decomposition and Symmetries

• Authors: Rabah W. Aldhaheri
• Venue: Multidimensional Systems and Signal Processing
• Year: 2004

In this paper we present a new and numerically efficient technique for designing 2-D linear phase octagonally symmetric digital filters using Schur decomposition method (SDM) and the diagonal symmetry of the 2-D impulse response specifications. This technique is based on two steps. First, the 2-D impulse response matrix is decomposed into a parallel realization of k sections, each comprising two cascaded linear phase SISO 1-D FIR digital filters. It is shown that using the symmetry property of the 2-D impulse response matrix and the fact that the left and right eigenspaces obtained by SDM are transpose of each other, the design problem of two 1-D digital filters is reduced to the design problem of only one 1-D digital filter in each section.In the second step, the 2-D linear phase FIR filter is converted to 2-D IIR filter. This is done by converting the constituent N-order 1-D FIR filters to an n-order IIR filters, where n N using the given model reduction algorithm. The reduced order IIR filters are obtained without computing the balancing transformation, but by finding the orthonormal eigenspaces associated with the largest eigenvalues of the cross-Gramian matrix WCO.Two design examples are given to illustrate the advantages of the proposed technique.