基于输入平衡实现的一类高效IIR数字滤波器结构

An input-balanced realization-based structure for efficient implementation of digital IIR filters

基于一种输入平衡实现,本文导出了一种简洁有效的IIR数字滤波器结构,并导出了传函灵敏度函数和舍入噪声增益的数学表达式.对于一个N阶的数字滤波器,该结构只需5N-1个乘法器,比归一化格型结构少了两个乘法器.对于全通系统,新结构的乘法器个数和舍入噪声增益都为4N,极大地降低了最佳状态空间实现具有的(N+1)2.通过仿真实例验证了所提结构对有限字长效益的高鲁棒性和实现的简洁性.

Based on an input-balanced state-space realization, this paper derives a novel structure for efficient implementation of digital IIR filters. Such a structure is very similar to a normalized lattice and, for an Nth order IIR filter, it possesses 5N - 1 non-trivial multipliers： two multipliers less than in a normalized lattice. Expressions for transfer function sensitivity measures and roundoff noise gain for the proposed structure are derived. Interest- ingly, it is shown that, when the filter is all-pass, the proposed structure requires 4N multiplications in order to compute one output sample. Moreover, the corresponding roundoff noise gain is 4N, much smaller than that of （N ＋ 1）a given by the classical minimum roundoff state-space realizations. Results of simulations performed show that the proposed structure outperforms many classical ones in terms of implementation efficiency and robustness against finite-word-length effects.