Design of linear phase IIR filter banks using eigenfilters

This paper presents a new method for linear phase IIR (infinite impulse response) two-band filter bank design with perfect reconstruction (PR). The method is based on the design of complex allpass filters. The resulting IIR filters can be real or complex depending on the parity of the allpass filter order N. The allpass filter coefficients are obtained from an eigenvector of a real, symmetric and definite positive matrix. The proposed matrix is partitioned to obtain four (N +1) × (N + 1) centrosymmetric submatrices. Consequently, if the minimum eigenvalue is unique the resulting filter coefficients form a symmetric sequence. Closed form equations for the entries of each centrosymmetric matrix are given. Different design examples illustrate the method.