Efficient iterative design of modified DFT filter banks

An iterative algorithm based on the Lagrange multiplier method is presented for designing modified discrete Fourier transform (MDFT) filter banks with perfect reconstruction (PR). The dominant work at each iteration is to solve a system of linear equations involving a symmetric block matrix. By exploiting its special structure, the block matrix is factored into the product of lower and upper triangular matrices, thus leading to improved efficiency. The main benefit of the proposed scheme is that it allows the efficient design of PR MDFT filter banks with a large number of channels and/or long prototype filters.