Design of linear phase M-channel perfect reconstruction FIR filter banks

We propose two approaches to design M channel nonparaunitary filter banks that satisfy perfect reconstruction (PR) and linear phase (LP) properties. In the first approach, the PR condition is imposed on only a high-pass filter. Although this method does not require nonlinear optimization, it has a demerit in that the order of a high-pass filter becomes high. In the second approach, two filters are optimized simultaneously using a Lagrange-Newton method. We can design PR filter banks that have the same length. The PR constraint is also formulated as a linear and nonlinear equation of the analysis filter coefficients. Finally, some design examples are included.