A Study on Auto-Regressive and Moving-Average Lattice Digital Filters

1.对于随机过程系统的输入输出信号，通过谱估计或线性预测得到传递函数。在本研究中，我们开发了模型辨识系统(模型辨识系统)，用自适应方法估计ARMA模型的时变参数。MIS的特征是预测误差之间的正交关系、新的逼近准则和通过对预测误差进行归一化而得到的稳定性判别。利用这些性质，我们可以很容易地设计出任意AR阶和任意MA阶的ARMA数字格型滤波器。提出了一种AR和ARMA模型并行处理的算法。利用该算法可以更快地综合ARMA数字格型滤波器。应用电路理论综合了适用于自适应数字信号处理的ARMA数字格型滤波器。也就是说，我们证明了作为模拟电路的分布恒定电路等价于波数字滤波器，并且它们等价于ARMA数字格型滤波器。通过等价性，我们给出了与给定的输入脉冲响应和自相关系数匹配或用最小二乘算法逼近的ARMA数字格型滤波器的综合方法。利用模拟电路与数字电路之间的等价关系，讨论了复系数电路的性质。在使用散射矩阵综合模拟和数字电路时，我们使用反射系数。复杂电路的反射系数有两种，即等匹配和共轭匹配。我们引入了一种适用于共轭匹配的伪传输线，并证明了利用这种伪传输线可以用达林顿综合法来综合无源复变传递函数。

1. For the input and output signals of a stochastic process system, the transfer function is obtained by spectrum estimation or linear prediction. In this reseearch, we have developed Model Identification System (MIS) to estimate time varying parameters of ARMA model with an adaptive method. MIS is characterized by orthogonal relationships among prediction errors, new criterion for an approximation and a stability discrimination obtained by normalizing the prediction errors. By these properties, we can easily design the ARMA digital lattice filter with an arebitrary AR order and an arbitrary MA order. We also have proposed an algorithm possible of parallel processing for AR and ARMA modeling. By the algorithm, we can synthesize ARMA digital lattice filter faster.2. We apple the circuit theory for the synthesis of ARMA digital lattice filter which is suitable for adaptive digital signal processing. That is, we have shown that the distributed-constant circuit, which is an analog circuit, is equivalent to the Wave Digital Filter, and that they are equivalent to ARMA digital lattice filter. By the equivalence, we have denoted the synthesis method of ARMA digital lattice filters which match to the given inpulse responses and autocorrelation coefficients, or which are approximated with the least square algorithm.3. We consider the properties of a complex coefficient circuit by using the equivalent relation between the analog circuit and the digital circuit. In synthesizing the analog and digital circuits with the scattering matrix, we use reflection coefficients. There are two kinds of reflection coefficients for the complex circuit, i.e. equal matching and conjugate matching ones. We have introduced a pseudo-transmission-line suitable for the conjugate matching, and we show that the passive complex transfer function can be synthesized with the Darlington synthesis by using the pseudo-transmission-lines.