Abstract: A novel design method for the prototype filters of a Near Perfect Reconstruction（NPR） Discrete Fourier Transform（DFT）modulated filter bank is proposed.The objective is derived from the output distortion induced by the filter bank，the aliased components that appear in the output，and the stopband energy of the prototype filters.By means of the particular structure of DFT modulated filter bank，minimizing the aliased components that appear in the output is simplified to minimizing the intra-channel aliasing，and minimizing the output distortion induced by the filter bank is approximately substituted by minimizing the output distortion of the adjacent three channels.It is shown that the design of prototype filters can be transformed into a simple nonlinear optimization problem.Compared with the current methods of DFT modulated filter bank，the design method proposed in this paper can generate filter banks with equivalent，even better performances，at the same time，owns a simple optimization formulation and considerable design flexibility.The simulation results verify the effectiveness of the method.

Key words: DFT, modulated filter bank, NPR, prototype filter

摘要： 提出了一种新的近似完全重构（NPR）离散傅立叶变换（DFT）调制滤波器组的原型滤波器设计方法。其优化的目标函数由滤波器组的输出混叠、输出失真及原型滤波器的阻带能量所导出。在此设计方法中，利用DFT调制滤波器组的特殊结构合理简化了滤波器组的输出混叠，输出失真。原型滤波器的设计最终被转化为一个简单的非线性优化问题。与目前的DFT调制滤波器组的设计方法相比，该方法提供了相当大的灵活性同时具有简单的优化描述。仿真结果证实了所提出的设计方法的有效性。

关键词: DFT, 调制滤波器组, NPR, 原型滤波器