Design of 2-dimensional linear phase perfect reconstruction FIR filter bank using Lagrange multiplier method

We present a design method of 2-dimensional (2D) linear phase (LP) perfect reconstruction (PR) FIR filter banks based on the Lagrange multiplier method. In M analysis filters, we first design M-1 analysis filters which have an LP property. Finally we design the Mth analysis filter with LP so that the overall system satisfy PR. Then the Mth analysis filter is optimized to have a good response while keeping PR based on the Lagrange multiplier method. By this method, 2D LP PR filter banks can be easily designed by only solving the simultaneous equation, although the order of the Mth analysis filter is higher than that of the others.