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为了推广数字滤波器的统计设计方法,本文提出了一种实现 ARMA 数字滤波器的群延迟特性的近似方法。因为在递归型群延迟滤波器中,分母系数列和分子系数列的排列顺序刚好相反,所以只要求得其中任一个系数列,就能相应地求得另一个系数列。在本近似法中,首先通过求复逆谱,将群延迟特性的近似问题转化为平方振幅特性的近似问题,再由线性预测方法,用 AR(全极型)滤波器模型求出近似的分母系数列,并由它的反向排列来得到分子系数列。因为主要设计程序采用了快速傅里叶变换和莱文森-德宾算法,所以和过去采用反复计算求解的方法相比,其求解的速度可大大提高,而且求得的近似系统稳定性容易得到保证,同时,在设计过程中还能直接求出实现敏感度低的递推型的系数列。作为本方法的应用以及等效群延迟的例子,本文给出了模拟雷达信号的处理结果。本文最后对设计具有大的群延迟特性的高阶滤波器的近似法所面临的困难等其它几个遗留问题进行了探讨。
In order to popularize the statistical design method of digital filter, this paper presents an approximate method to realize the group delay characteristic of ARMA digital filter. Because in the recursive group delay filter, the order of denominator coefficient series and molecular coefficient series is just the opposite, so as long as one of the coefficient series is obtained, another coefficient series can be obtained accordingly. In the approximation method, the approximate problem of the group delay characteristic is transformed into the approximation problem of the square amplitude characteristic by the complex inverse spectrum first, and then the approximate denominator is obtained by the linear prediction method using the AR (all-pole) filter model Coefficient column, and by its reverse arrangement to get the molecular coefficient column. Because the main design process uses the Fast Fourier Transform and the Levinson-Durbin algorithm, the speed of solution can be greatly improved and the approximate system stability obtained can be easily obtained compared with the method of iterative calculation in the past Guarantee, at the same time, in the design process can also directly find the recursive coefficient series to achieve low sensitivity. As an example of the application of this method and the equivalent group delay, the processing results of the simulated radar signal are given in this paper. In the end of this paper, we discuss some remaining problems such as the difficulty of approximating the high-order filter with large group delay characteristics.