可变带宽FIR低通滤波器设计和RAG算法系数综合

The Design of Variable Bandwidth FIR Low Pass Filter and Synthesis Considering RAG Algorithm for A Coefficient

提出使用简化加法器图算法综合可变带宽FIR数字滤波器。首先使用谱参数的方法建立可变带宽、线性相位的FIR低通数字滤波器的系统函数,通过使用加权最小均方的方法,得到了滤波器系数的最优表达式。然后基于可变滤波器结构为定系数FIR子滤波器线性组合的特点,提出使用简化加法器图算法综合其硬件结构。该算法生成一种能最大程度地利用系数之间共享特性的加法器流图,使用较少的加法器个数和加法次数实现系数相乘。最后设计实例证明了可变带宽的有效性和该算法的高效性。

A reduced adder graph algorithm is proposed to synthesis the variable bandwidth FIR digital filter. Firstly, it is established that the system function of the variable bandwidth and linear-phase FIR low pass digital filter using the method of spectral parameter, and the method of weighted least- squared is used to calculate the optimal expression of the filter coefficients. Then based on the character the structure of variable digital filter is the linear combination of the fixed-coefficient FIR sub - fil- ter, it is proposed to synthesis the hardware structure with the reduced adder graph arithmetic. It is an arithmetic which could select an adder graph that can be maximally sharable with the remaining coefficients, and implement the multiplication of coefficients with fewer adders and add times. Lastly, design examples are provided to illustrate the validity of the variable bandwidth and the effectiveness of the arithmetic.