两通道正交图滤波器组设计新算法

New method for designing the two-channel orthogonal graph filter bank

针对两通道正交图滤波器组频率特性差的问题,提出了一种基于二阶泰勒近似的迭代算法.首先,该算法将两通道正交图滤波器组的设计问题归结为一个带约束优化问题.将图滤波器组的重构误差作为目标函数,滤波器的阻带衰减作为约束函数;然后,通过泰勒近似将高度非线性非凸的目标函数转化为关于增量的凸的二次函数,将非凸优化问题近似为凸的优化问题;最后,采用迭代方法求解该优化问题.仿真结果表明,与伯恩斯坦多项式逼近的算法相比,新算法设计的两通道正交图滤波器组重构误差减小了约1个数量级,信噪比提高了约8dB.

An iterative algorithm based on sccond-ordcr approximation of Taylor’s series is proposed to overcome the problem that the two channel orthogonal graph filter bank possesses poor frequency characteristic.First,the design problem is formulated into a constrained optimization problem,whose objective function is the reconstruction error of the two channel orthogonal graph filter bank,and the constraint function is the stopband attenuation.Then,by means of the Taylor approximation,the highly nonlinear nonconvcx objective function is approximately transformed into a convex quadratic function with respect to increments.Thus,the nonconvcx optimization problem is approximated to a convex optimization problem.Finally,an iterative technique is used to solve the optimization problem.Simulation results show that the reconstruction error of the two channel orthogonal graph filter bank obtained by the new method is approximately one order of magnitude lower than that by the Bernstein polynomial approximation algorithm and that the improvement on the reconstruction error is about 8dB.