这个多采样速率率滤波器组如何实现？

[liangzhang21]

该图来自：Masataka Goto 2004 年"A real-time music-scene-description system: predominant-F0 estimation for detecting melody and bass lines in real-world audio signals" 一文中的3.1.1章节。

相关描述如下：

At each level of the binary branches, the audio signal is down-sampled by a decimator that consists of an anti-aliasing filter (an FIR lowpass filter (LPF)) and a 1/2 down-sampler. The cut-off frequency of the LPF in each decimator is 0.45 fs, where fs is the sampling rate at that branch.

很困惑 滤波和降采样率的先后顺序？请大佬们教学一下，谢谢了