基于树状图的波形数字滤波器拓扑结构优化方法

针对常规波形数字滤波器（wave digital filter，WDF）拓扑结构表达效率低下、结构易混乱的问题，本文利用适配器的可拆分性，提出基于WDF二叉树的拓扑结构表达方法，使等效电路结构清晰直观，从WDF二叉树的形态可迅速获知等效电路的模块并行度、最长路径等关键信息.此外，本文结合WDF端口适配器的端口对称性，进一步提出WDF二叉树的优化方法.通过对满足要求的结点及附属子叶进行位置交换，令二叉树更为扁平、缩短"入射-反射"过程的最大路径长度，使WDF-FPGA仿真系统的模块并行度和仿真速度得到提升.电路仿真模型优化后的反射步长减少42.86%、入射步长减少38.9%，总运算时间降至0.366 ms. 

A Topology Optimization Method of Waveform Digital Filter Based on Dendrogram

In this paper,an optimizing methodology for wave digital filter (WDF)equivalent circuit was proposed.This binary tree based method can simplify simulation system and improve system performance on speed.The WDF with binary tree representation was provided with a clear and intuitive structure to solve the low expressing efficiency issue in traditional WDF topology.The shape of this tree can directly indicate essential information of WDF equivalent circuit,such as module parallelism and the longest path. Moreover, considering the port symmetry of the WDF adapter,an optimizing methodology was presented for WDF binary tree to reduce processing steps in each simulating cycle and improve the overall performance of simulation.The optimization results show that, the reflection step length can be reduced by 42.86%,while the incidence step length can be reduced by 38.9%,the total operation time can be reduced to 0.3 6 6 ms.