带包络约束的优化滤波器设计方法

A Design Approach to Optimal Filter with Envelope-Constrained

对信道均衡、雷达或声纳脉冲压缩等应用领域中要求满足波形条件且使输出噪声增益最小化的滤波器设计问题进行了研究。用波形包络约束表达式和极值条件可以准确地描述滤波器的性能要求,从而将该设计问题转化为半无限二次凸规划问题进行分析。利用Lagrangian对偶理论和Carathéodory维度理论把半无限二次凸规划问题转化成等价的易于求解的有限维对偶优化问题,并给出了求解有限维对偶优化问题的迭代算法,设计实例表明了此方法的有效性。

In this paper, we give a thoroughly study on the approach to design of linear time-invariant filter with minimal output noise enhancement and output signal shape constrained to lie within prescribed upper and lower bounds envelope. With the shape envelope inequality constraints and optimal value conditional expression, the performance requirements of filter can be mathematically formulated as optimization problem. Then the envelope constrained optimal filter design problem can be transform into an QP problem with a convex quadratic cost function and semi-infinite number of linear inequality constraints. Utilizing Lagrangian＇s dual and Carathéodory＇s dimensionality theorem, the semi-infinite convex quadratic programming problem is converted into an equivalent finite optimization dual problem, which can be solved by generic optimization methods. Moreover, iterative algorithm for solving equivalent finite optimization dual problem is presented. By a design example, the theory and method are proved most feasible.