Design of 2-D Perfect Reconstruction Diamond-Shaped and Fan-Shaped FIR Filter Banks

The paper gives a design method of two-channel FIR diamond-shaped and fan-shaped filter banks, which are the important part of directional filter banks. Firstly, we make an analysis of 2D two-channel filter banks where the perfect reconstruction condition is derived. On this basis, the 2D maximally flat filter is adopted to be the mapping filter and the 1D two-channel filter bank is constructed to satisfying the perfect reconstruction condition. Afterwards the 1D two-channel filter bank is mapped into the 2D diamond-shaped filter bank using the method of variable substitution. Finally the 2D fan-shaped filter bank is obtained by modulating the diamond-shaped filter bank.