Architectures for IIR digital filters using stochastic computing
Architectures for IIR digital filters using stochastic computing
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使用随机计算的 IIR 数字滤波器架构
DOI：
10.1109/iscas.2014.6865143
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Yin Liu
中科院分区：
文献类型：
--
作者：
K. Parhi;Yin Liu
本文讨论了使用随机计算实现IIR数字滤波器。随机计算需要较少的逻辑门，并且具有固有的容错性。因此，这些结构非常适合深亚微米技术。虽然用随机计算实现FIR数字滤波器很容易，但实现IIR数字滤波器却不是简单的。随机逻辑假定输入信号的独立性；然而，IIR数字滤波器的反馈导致输入信号相互关联，违反了独立性假设。本文的新颖之处在于证明，尽管IIR滤波器中存在反馈，但这些滤波器可以使用随机逻辑实现。随机实现的关键是选择IIR滤波器结构，其中状态是正交的，因此是不相关的。提出了两种随机IIR数字滤波器的结构。这两种体系结构都基于状态正交的晶格滤波器表示。第一种是基于从晶格滤波器结构导出的IIR滤波器的状态空间描述。第二种是基于将晶格IIR数字滤波器转换为等效形式，该形式可以利用我们先前工作中开发的用于内积计算的新型缩放方法。我们的实验结果表明，与使用直接形式IIR滤波器的随机实现相比，我们提出的两种随机IIR数字滤波器架构可以使输出误差与信号功率比降低一到两个数量级。此外，对于高阶滤波器，当随机直接形式结构不能正确工作时，基于状态空间和晶格的随机IIR数字滤波器总是以功能正确的方式过滤输入信号。
This paper addresses implementation of IIR digital filters using stochastic computing. Stochastic computing requires fewer logic gates and is inherently fault-tolerant. Thus, these structures are well suited for deep sub-micron technologies. While it is easy to realize FIR digital filters using stochastic computing, implementation of IIR digital filters is non-trivial. Stochastic logic assumes independence of input signals; however, the feedback in IIR digital filters leads to correlation of input signals and the independence assumption is violated. The novelty of this paper lies in demonstrating that, despite the feedback in IIR filters, these filters can be implemented using stochastic logic. The key to stochastic implementation is selection of an IIR filter structure where the states are orthogonal and are, therefore, uncorrelated. Two architectures are presented for stochastic IIR digital filter. Both architectures are based on the lattice filter representation where the states are orthogonal. The first is based on a state-space description of the IIR filter derived from the lattice filter structure. The second is based on transforming the lattice IIR digital filter into an equivalent form that can exploit the novel scaling approach developed in our prior work for inner product computations. Our experimental results show that the two proposed architectures for stochastic IIR digital filters can lead to one to two orders of magnitude reduction in the output error-to-signal power ratio, compared to stochastic implementations using direct-form IIR filters. Furthermore, for higher-order filters, while stochastic direct-form structures fail to function correctly, the state-space and lattice based stochastic IIR digital filters always filter the input signals in a functionally correct manner.