余弦调制子带滤波器组迭代设计的改进算法

摘要

余弦调制子带滤波器组的设计可以转化成一个高维非线性优化问题,传统遮代设计方法虽然避免了复杂的直接求解过程,但是其混叠误差的抑制依赖于滤波器阻带衰减的大小,设计出的滤波器往往阶数过高.本文提出了一种改进的子带余弦调制滤波器组迭代设计算法,其代价函数除了包括子带系统响应和子带滤波器阻带能量之外,还添加了系统一次混叠项因子,更好地抑制了混叠误差.本文将新的代价函数表示成滤波器系数的二次函数形式,并推导出其极值点的闭合解表达式.算法保留了传统迭代方法逐渐逼近极值点的思想,简单易于实现.仿真结果表明与传统迭代设计方法相比,本文算法获得的子带滤波嚣组具有更小的混叠误差和更低的滤波器阶数.%The design of cosine-modulated subband filter banks can be converted to a high-dimension nonlinear optimization problem, but the orders of designed fitter banks are generally too high, because of its aliasing error controll relied by the stop band attenuation. A modified iteration design method for cosine-modulated filter banks (CMFB) is proposed. Its new cost function consists of system response, stopband energy and the first aliasing factor which is added to eliminate the aliasing error more effectively. The cost function is formulated as a quadratic function whose minimum point can be obtained using a closed-form solution. The minimum point is approached by iteration in the algorithm, which is simpler and more realizable than the direct optimization method. Simulation results demonstrate that the algorithm can be used to design the subband filter banks with less aliasing error and shorter length, comparing with the conventional iteration design method.