一类冗余比为2的二维DFT调制滤波器组的设计

本文构建了一类冗余比为2的二维线性相位的双原型离散傅立叶变换（DFT）调制滤波器组。利用原型滤波器的多相位分解，推导出了该滤波器组的完全重构(PR)条件。基于该PR条件，我们将滤波器组的设计归结为一个关于原型滤波器的多相位分量的无约束优化问题。由于原型滤波器是线性相位的，多相位分量之间具有一定的关系，因此我们可以简化该优化问题。仿真结果验证了滤波器组PR条件的正确性。同时，仿真表明了优化算法的有效性，设计所得的滤波器组重构误差很小、频率特性较好，基本满足实际应用的需要。 

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.