为解决传统数字滤波器在有限精度实现时因有限字长(Finite Word Length,FWL)效应导致滤波器性能下降的问题,提出一种L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法.推导前向差分算子数字滤波器结构传输函数及其等效状态空间实现...为解决传统数字滤波器在有限精度实现时因有限字长(Finite Word Length,FWL)效应导致滤波器性能下降的问题,提出一种L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法.推导前向差分算子数字滤波器结构传输函数及其等效状态空间实现,根据可控及可观格莱姆矩阵得到基于相似变换矩阵的L_(2)灵敏度表达式,并进行稀疏化校准,将L_(2)灵敏度最小化问题转换为凸函数求最值问题,求导得到L_(2)灵敏度最小化表达式,代回即得前向差分算子数字滤波器的稀疏化状态空间实现.仿真结果表明,所提方法设计的数字滤波器具有更好的抗FWL效应.展开更多
This article deals with two important issues in digital filter implementation： roundoff noise and limit cycles. A novel class of robust state-space realizations, called normal realizations, is derived and characteriz...This article deals with two important issues in digital filter implementation： roundoff noise and limit cycles. A novel class of robust state-space realizations, called normal realizations, is derived and characterized. It is seen that these realizations are free of limit cycles. Another interesting property of the normal realizations is that they yield a minimal error propagation gain. The optimal realization problem, defined as to find those normal realizations that minimize roundoff noise gain, is formulated and solved analytically. A design example is presented to demonstrate the behavior of the optimal normal realizations and to compare them with several well-known digital filter realizations in terms of minimizing the roundoff noise and the error propagation.展开更多
The complexity of linear, fixed-point arithmetic digital controllers is investigated from a Kolmogorov-Chaitin perspective. Based on the idea of Kolmogorov-Chaitin complexity, practical measures of complexity are deve...The complexity of linear, fixed-point arithmetic digital controllers is investigated from a Kolmogorov-Chaitin perspective. Based on the idea of Kolmogorov-Chaitin complexity, practical measures of complexity are developed for statespace realizations, parallel and cascade realizations, and for a newly proposed generalized implicit state-space realization. The complexity of solutions to a restricted complexity controller benchmark problem is investigated using this measure. The results show that from a Kolmogorov-Chaitin viewpoint, higher-order controllers with a shorter word-length may have lower complexity and better performance, than lower-order controllers with longer word-length.展开更多
针对HRTF(Head Related Transfer Function,头相关传输函数)滤波器硬件实现时产生的FWL(Finite WordLength,有限字长)效应问题,提出了一种HRTF滤波器的高效实现方法。这种方法采用一种新的YWB(Yule-Walker+Balance Model Truncation)算...针对HRTF(Head Related Transfer Function,头相关传输函数)滤波器硬件实现时产生的FWL(Finite WordLength,有限字长)效应问题,提出了一种HRTF滤波器的高效实现方法。这种方法采用一种新的YWB(Yule-Walker+Balance Model Truncation)算法实现降阶,应用正规实现对抗FWL效应,并应用矩阵的Schur分解达到结构稀疏化。仿真结果说明了YWB算法显著的降阶效果,并说明了这种高效实现方法不仅能对抗FWL效应,而且大大降低了实现复杂度。展开更多
文摘为解决传统数字滤波器在有限精度实现时因有限字长(Finite Word Length,FWL)效应导致滤波器性能下降的问题,提出一种L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法.推导前向差分算子数字滤波器结构传输函数及其等效状态空间实现,根据可控及可观格莱姆矩阵得到基于相似变换矩阵的L_(2)灵敏度表达式,并进行稀疏化校准,将L_(2)灵敏度最小化问题转换为凸函数求最值问题,求导得到L_(2)灵敏度最小化表达式,代回即得前向差分算子数字滤波器的稀疏化状态空间实现.仿真结果表明,所提方法设计的数字滤波器具有更好的抗FWL效应.
基金the National Nature Science Foundation of China (60774021)
文摘This article deals with two important issues in digital filter implementation： roundoff noise and limit cycles. A novel class of robust state-space realizations, called normal realizations, is derived and characterized. It is seen that these realizations are free of limit cycles. Another interesting property of the normal realizations is that they yield a minimal error propagation gain. The optimal realization problem, defined as to find those normal realizations that minimize roundoff noise gain, is formulated and solved analytically. A design example is presented to demonstrate the behavior of the optimal normal realizations and to compare them with several well-known digital filter realizations in terms of minimizing the roundoff noise and the error propagation.
文摘The complexity of linear, fixed-point arithmetic digital controllers is investigated from a Kolmogorov-Chaitin perspective. Based on the idea of Kolmogorov-Chaitin complexity, practical measures of complexity are developed for statespace realizations, parallel and cascade realizations, and for a newly proposed generalized implicit state-space realization. The complexity of solutions to a restricted complexity controller benchmark problem is investigated using this measure. The results show that from a Kolmogorov-Chaitin viewpoint, higher-order controllers with a shorter word-length may have lower complexity and better performance, than lower-order controllers with longer word-length.
文摘针对HRTF(Head Related Transfer Function,头相关传输函数)滤波器硬件实现时产生的FWL(Finite WordLength,有限字长)效应问题,提出了一种HRTF滤波器的高效实现方法。这种方法采用一种新的YWB(Yule-Walker+Balance Model Truncation)算法实现降阶,应用正规实现对抗FWL效应,并应用矩阵的Schur分解达到结构稀疏化。仿真结果说明了YWB算法显著的降阶效果,并说明了这种高效实现方法不仅能对抗FWL效应,而且大大降低了实现复杂度。
