The design of filter banks, which is a frequently used operator for many practical applications, has been widely reported in the literature. The requirements of using extensive mathematical manipulations for finding computationally efficient structures of filter banks have imposed severe difficulties for those who lack sufficient mathematical background. This paper is to report procedures of deriving computationally efficient filter bank structures by using a few graphic transformations of equivalent multi-rate operations. It is seen that these procedures used in the derivation process are elegantly simple and straight forwards in concept. In particular, these procedures can be flexibly used to find the computationally efficient structures of both maximally decimated ($p=1$) and non-maximally decimated ($p>1$) filter banks, where p is the oversampling factor. For the non-maximally decimated filter banks, the computational complexity needed by our derived structure is less than that needed by the structures reported in the literature.

滤波器组的设计是许多实际应用中经常使用的算子，已在文献中广泛报道。对于那些缺乏足够数学背景的人来说，使用广泛的数学运算来寻找滤波器组的计算效率结构的要求已经带来了严重的困难。本文将报告通过使用等效多速率操作的一些图形转换来导出计算效率高的滤波器组结构的过程。可以看出，推导过程中使用的这些程序在概念上非常简单和直接。特别是，这些过程可以灵活地用于找到最大抽取（$磷=1$) 和非最大抽取 ($磷>1$) 滤波器组，其中p是过采样因子。对于非最大抽取滤波器组，我们导出的结构所需的计算复杂度低于文献中报告的结构所需的计算复杂度。