Downsampling with Anti-Aliasing

Figure 9.19: Processing in one filter-bank analysis channel.

In OLA, the hop size $R$ is governed by the COLA constraint

$$\sum_{m=-\infty}^\infty w(n+mR) = \hbox{constant}$$ (10.26)

In FBS, $R$ is the downsampling factor in each of the filter-bank channels, and thus the window $w$ serves as the anti-aliasing filter (see Fig.9.19). We see that to avoid aliasing, $W(\omega)$ must be bandlimited to $(-\pi/R, \pi/R)$ , as illustrated schematically in Fig.9.20.

Figure 9.20: Schematic illustration of a window transform that suppresses all aliasing.