为了设计一维DFT调制滤波器组,采用一种线性规划算法将滤波器组的性能指标数学化为关于原型滤波器的乘积滤波器的函数,滤波器组的设计问题归结为一个以乘积滤波器为优化变量的线性规划问题.借助线性规划的求解方法,设计最优的乘积滤波器,通过因式分解求解原型滤波器.新算法避免了迭代算法对初值敏感的问题.仿真实验表明,相比于传统算法,新算法设计的滤波器组具备更好的整体性能,其中,重构误差降低约5 dB,阻带衰减改善约6 dB.%An linear program algorithm is adopted to design ID DFT modulated filter banks. First, the performance measures of the filter bank are converted into functions of the product filter of the analysis filters. Then, the design problem is transformed into a linear program problem with respect to the product filter. The optimal product filter can be efficiently solved from the linear program problem. Finally, the analysis filter can be obtained from the product filter using spectral decomposition. The algorithm avoids the sensitivity to the initial point. The simulations show that compared with the traditional method, the new algorithm can lead to filter bank with improved performance. The improvement of the reconstruction error is about 5 dB and that of stopband attenuation is about 6 dB.
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