基于梯度下降的可变分数时延滤波器优化方法  

Optimization method for variable fractional delay filters based on gradient descent

作　　者：庄陵[1,2,3] 郝汉杰 ZHUANG Ling;HAO Hanjie(School of Communications and Information Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;Engineering Research Center of Mobile Communication,Ministry of Education,Chongqing 400065,China;Chongqing Key Laboratory of Mobile Communication Technology,Chongqing 400065,China)

机构地区：[1]重庆邮电大学通信与信息工程学院,重庆400065 [2]移动通信教育部工程研究中心,重庆400065 [3]移动通信技术重庆市重点实验室,重庆400065

出　　处：《通信学报》2025年第4期121-128,共8页Journal on Communications

基　　金：重庆市教育委员会科学技术研究基金资助项目(No.KJQN202200617)。

摘　　要：针对可变分数时延滤波器低失真传输需求,提出一种基于梯度下降并结合均方根传播的优化方法。首先,通过矩阵形式推导目标函数与梯度表达式,利用历史与当前梯度信息的指数移动平均来调整步长。其次,更新权重时引入上次迭代残差的协方差矩阵,以进一步提高滤波器频响特性与理想特性的逼近程度。最后,从复杂度和误差方面与现有方法进行对比。仿真结果表明,与传统加权最小二乘法相比,所提方法在保证局部幅度与群时延精度的同时,归一化均方根误差有效降低34.36%。In order to address the requirements for low distortion transmission of variable fractional delay filters,an optimization method based on gradient descent and root mean square propagation was proposed.Firstly,the matrix form of the objective function and gradient expressions were derived,and an exponential moving average was used to adjust the step size based on historical and current gradient information.Secondly,the weight update mechanism incorporated the residual covariance matrix from previous iterations,thereby enhancing the approximation between the frequency response of the filter and the ideal response.Finally,comparisons with existing methods were conducted on the aspects of complexity and error.Simulation results demonstrate that,compared with the traditional weighted least square method,the proposed method effectively reduces the normalized root mean square error by 34.36%while maintaining high accuracy in both local amplitude and group delay.

关 键 词：可变分数时延滤波器 低失真 梯度下降 均方根传播 归一化均方根误差 

分 类 号：TN713.7[电子电信—电路与系统]