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Structures for anticausal inverses and application in multirate filter banks

机译:反因果逆结构及其在多速率滤波器组中的应用

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摘要

Anticausal or time-reversed inversion of digital filters has gained importance in the implementation of digital filter banks. Anticausal inversion has, in the past, been shown to be possible by using block processing with appropriate state initialization. With (A, B, C, D) denoting the state-space description of a structure implementing a filter G(z), the anticausal inverse can be essentially regarded as a filter structure having an inverted state-space description, which we denote as (Aˆ, Bˆ, Cˆ, Dˆ). It is usually not efficient to implement the state-space equations given by (Aˆ, Bˆ, Cˆ, Dˆ) directly because of excessive multiplier count. Rather, one seeks to find an efficient structure having the inverse description (Aˆ, Bˆ, Cˆ, Dˆ). While this can be done by inspection in simple cases such as the direct-form structure, systematic procedures for other important structures have yet to be developed. We derive anticausal inverse structures corresponding to several standard IIR filter structures such as the direct-form, cascade-form, coupled-form, and the entire family of IIR lattice structures including the tapped cascaded lattice. We introduce the notion of a causal dual, which we find convenient in the derivations. We show that the limit-cycle free property of the original structure is inherited by the causal dual in some but not all cases.
机译:在数字滤波器组的实现中,数字滤波器的因果关系或时间反转是非常重要的。过去,通过使用具有适当状态初始化的块处理已显示出因果反转是可能的。用(A,B,C,D)表示实现滤波器G(z)的结构的状态空间描述,反因果反函数本质上可以看作是具有反向状态空间描述的滤波器结构,我们将其表示为(A B C D)。由于乘数过多,直接实现由(Aˆ,Bˆ,Cˆ,Dˆ)给出的状态空间方程通常效率不高。相反,人们试图找到一种具有相反描述(A 1,B 4,C 3,D 4)的有效结构。尽管可以在简单的情况下(例如直接形式的结构)通过检查来完成,但尚未开发其他重要结构的系统程序。我们推导了与几种标准IIR滤波器结构相对应的反因果逆结构,例如直接形式,级联形式,耦合形式以及包括分接级联晶格在内的整个IIR晶格结构家族。我们介绍了因果对偶的概念,在推导中我们发现它很方便。我们表明,在某些但并非全部情况下,原始结构的无极限环属性是因果对偶继承的。

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  • 作者单位
  • 年度 1998
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  • 原文格式 PDF
  • 正文语种 {"code":"en","name":"English","id":9}
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