基于线性迭代的DFT调制滤波器组的设计算法

Design of DFT modulated filter banks via linearizing iterative approach

该文研究了单原型的DFT调制滤波器组的设计方法。在该方法中,滤波器组的设计问题被归结为一个无约束的优化问题,其目标函数为滤波器组的传递失真、混叠失真和原型滤波器的阻带能量的加权和。结合线性化方法,原型滤波器通过迭代求解。在单步迭代中,原型滤波器的系数通过解析式求解得到。仿真表明,与传统的设计算法相比,本文方法设计所得的DFT调制滤波器组重构误差减小了约40dB,阻带衰减提高了约2dB。并且新算法的计算复杂度明显低于传统算法。

In this paper, the design of the single-prototype DFT modulated filter l^ank is investigated. The design is formulated as an unconstrained optimization whose objective function is the weighted sum of the transfer function distortion and the aliasing distortion of the fiilter banki and the stopband energy of the prototype filter （PF）. In terms of the linearization approach, the PF is iteratively solved, and at each iteration its coefficients are obtained analytically. Numerical examples show that, compared with the conventional algorithm, the DFT modulated filter bank designed by the proposed algorithm achieyes about 40dB improvement on the reconstruction error and about 2dB improvement on the stopband attenuation. Moreover, the proposed algorithm has much lower computational cost than the traditional method.