一种设计DFT调制滤波器组的新算法

针对离散傅里叶变换(DFT)调制滤波器组的设计较为复杂的缺点，提出了一种基于双迭代的设计算法．该算法将设计问题归结为一个简单的无约束优化问题，其目标函数是滤波器组的传递失真和原型滤波器阻带能量的加权和．由于该目标函数是关于分析和综合原型滤波器的双二次函数，因此优化问题可以利用双迭代机制来有效求解．在每一步迭代中，一个原型滤波器被确定，另一个原型滤波器可以通过解析式求解．仿真实验表明，相比于传统的设计算法，新算法计算复杂度低，并且设计的滤波器组传递失真减小了约16dB，重构误差减小了约1dB．

Novel method for designing DFT modulated filter banks

A design algorithm is proposed based on the bi-iterative scheme, due to the difficulty of designing the discrete Fourier transform (DFT) modulated filter bank. The design of the filter bank is formulated as an unconstrained optimization whose objective function is the weighted sum of the transfer distortion and the stopband energy of the prototype filters(PFs). Since the objective function is a bi-quadratic function of analysis and synthesis PFs, the optimization problem can be efficiently solved by using the bi-iterative scheme. At each iteration, one of the PFs is fixed and the other can be solved analytically. Numerical examples show that the computational cost of the proposed method is lower than that of the traditional method. Furthermore the transfer distortion of the filter bank obtained by the proposed method is approximately 16dB lower than that of the filter bank designed by the traditional method and the improvement on the reconstruction error is about 1dB.