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1. 发明授权

US4188667A ARMA filter and method for designing the same 失效
标题翻译： ARMA滤波器及其设计方法
公开(公告)号：US4188667A
公开(公告)日：1980-02-12
申请号：US852917
申请日：1977-11-18
申请人： Daniel Graupe , Aloysius A. Beex , G. Donald Causey
发明人： Daniel Graupe , Aloysius A. Beex , G. Donald Causey
IPC分类号： H04R25/04 , H03H11/04 , H03H17/02 , H03H17/04 , H04R25/00 , G06F15/34
CPC分类号： H04R25/505 , H03H17/0258 , H03H17/04 , H04R25/453
摘要： A near minimum order ARMA type recursive filter with guaranteed stability and convergence is provided together with a method for obtaining the parameters of such filter. The amplitude/frequency response of the filter approximates an arbitrarily selected frequency spectrum of amplitude, and the phase response approximates a substantially linear function of frequency with an arbitrarily selected slope because the parameters are identified, off-line, using a minimization process that minimizes an integral error norm. The first step involves performing an inverse discrete Fourier transform of the arbitrarily selected frequency spectrum of amplitude to obtain a truncated sequence of coefficients of a stable, pure moving-average filter model, i.e., the parameters of a non-recursive filter model. The truncated sequence of coefficients, which has N+1 terms, is then convolved with a random sequence to obtain an output sequence associated with the random sequence. A time-domain, convergent parameter identification is then performed, in a manner that minimizes an integral error function norm, to obtain the near minimum order parameters .alpha..sub.i and .beta..sub.j of the model having the desired amplitude- and phase-frequency responses, the parameters satisfying the relationship: ##EQU1## where: .alpha..sub.i is the ith auto-regressive parameter, and .beta..sub.j is the jth moving-average parameter, respectively, of an ARMA-type recursive filter; n and m denote the order of the auto-regressive and the moving-average parts of the ARMA model, respectively; y.sub.k and u.sub.k are associated elements of the kth element of the output sequence and the random sequence, respectively; k is an integer; and v is a shift integer selected to provide the desired slope of the phase response given by 2.pi.(v-N/2).
摘要翻译：提供具有保证稳定性和收敛性的近最小订单ARMA类型递归滤波器以及用于获得这种滤波器的参数的方法。滤波器的幅度/频率响应近似于任意选择的幅度频谱，并且相位响应以任意选择的斜率近似于频率的基本上线性的函数，因为参数被离线地识别，使用最小化处理使得积分误差范数。第一步涉及执行任意选择的振幅频谱的离散傅里叶逆变换，以获得稳定的纯移动平均滤波器模型的截断序列，即非递归滤波器模型的参数。具有N + 1项的截断的系数序列然后与随机序列进行卷积以获得与随机序列相关联的输出序列。然后以最小化积分误差函数范数的方式执行时域收敛参数识别，以获得具有期望幅度和相位频率响应的模型的近似最小阶次参数αi和βj，满足以下关系的参数：其中：αi是第i个自回归参数，βj分别是ARMA型递归滤波器的第j个移动平均参数; n和m分别表示ARMA模型的自回归和移动平均部分的顺序; yk和uk分别是输出序列的第k个元素和随机序列的相关元素; k是整数; 并且v是选择为提供由2π（v-N / 2）给出的相位响应的期望斜率的移位整数。

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