Design of two-dimensional DFT modulated filter banks with redundancy ratio two

In this paper, one type of two-dimensional (2-D) doubleprototype and linear phase DFT modulated filter banks with redundancy ratio two is constructed. In terms of the 2-D polyphase decomposition of prototype filters, the perfect-reconstruction (PR) condition of the filter banks is derived. Based on the PR condition, the design of the filter banks is formulated as an unconstrained optimization of the polyphase components of the two prototype filters. Due to the linearphase property of the prototype filters, there are some relations between these polyphase components Thus we can simplify the optimization problem with about half of the polyphase components.The correctness of the PR condition is verified by the numerical results Meanwhile, the numerical examples show the efficiency of the optimization procedure. The proposed algorithm can lead to non-separable 2-D double-prototype linear-phase DFT modulated filter banks with low reconstruction error and fine frequency property, which can meet the demand of the most applications