摘要
基于拉格朗日乘子法,该文提出一种2维修正离散傅里叶变换调制滤波器组的迭代设计方法。在每次迭代中,原型滤波器的设计描述成一个约束为2次函数的2次规划问题。引入拉格朗日乘子法将问题转化为无约束的优化问题,通过求解线性矩阵方程得到优化问题的解。针对矩阵方程中的系数矩阵的特点,运用块LU分解,显著降低了运算复杂度。仿真实验表明,与现有的设计方法相比,该文方法设计得到的2维修正离散傅里叶变换调制滤波器组的重构误差和阻带衰减均有较大的改善。
Base on Lagrange multiplier method, an iterative algorithm is proposed to design the two-dimensional modified Discrete Fourier Transform （DFT） modulated filter bank. In each iteration, the design problem is described as a Quadratically Constrained Quadratic Program （QCQP）. The Lagrange multiplier method is then employed to transform the constrained problem into an unconstrained one, the solution of which is obtained by solving a set of linear equations. By analyzing the coefficient matrix, block LU factorization is applied to considerably reduce the computational complexity. Numerical results and comparison with the existing methods demonstrate the improved performance of the proposed scheme, including the reconstruction error and stopband attenuation.
出处
《电子与信息学报》
EI
CSCD
北大核心
2017年第5期1261-1265,共5页
Journal of Electronics & Information Technology
基金
国家自然科学基金(61261032)~~
关键词
2维修正滤波器组
离散傅里叶变换调制
迭代优化
拉格朗日乘子法
块LU分解
Two-dimensional modified filter bank
DFT modulated
Iteration optimization
Lagrange multiplier method
Block LU factorization
