低延迟有限冲击响应滤波器约束最小二乘设计

针对具有低群延迟的非线性相位有限冲击响应滤波器的设计问题,采用在极小化复数误差能量的同时对复数误差和相位误差进行约束的方法,既可以得到凸的约束区域,又可以对幅值误差和相位误差进行独立控制.将具有给定相位误差的低通滤波器的最小二乘设计方法扩展到高通和带通滤波器的设计,引入左边和双边S形相位误差上界约束函数对高通和带通滤波器的相位误差进行约束,来抑制带边附近群延迟误差大的效应.应用改进的Goldfarb-Idnani算法求解由复数误差和相位误差约束最小二乘设计问题产生的半无穷正定二次规划.设计例子表明,该设计方法对减小滤波器的群延迟误差非常有效.

Constrained least square design of finite impulse response filter with reduced group delay

The constrained least square design of nonlinear phase finite impulse response filter with reduced group delay was considered. By minimizing the complex error energy and imposing the constraints on the complex approximation error and the phase error, the convex feasible region can be obtained, and the magnitude error and the phase error can be independently controlled. The least square method for low pass filter with given phase error was extended to the design of high pass and band pass filters. The left sided and double sided sigmoid upper bound functions were introduced to constrain the phase error of high pass and band pass filters in order to reduce the group delay error near the bandedges. An improved  Goldfarb Idnani algorithm was applied to solve the semi infinite positive definite quadratic programming problem resulted from the constrained least square design. Design examples demonstrate that the method is effective to the reduction of group delay error of the designed filter.