Example: Polyphase Analysis of the STFT with 50% Overlap, Zero-Padding, and a Non-Rectangular Window

Figure: Polyphase representation of the STFT with a more general window and $M/2$ hop size ($50$ % overlap).

Figure 11.26 illustrates how a window and a hop size other than $N$ can be introduced into the polyphase representation of the STFT. The constant-overlap-add of the window $w(n)$ is implemented in the synthesis delay chain (which is technically the transpose of a tapped delay line). The downsampling factor and window must be selected together to give constant overlap-add, independent of the choice of polyphase matrices $\bold{E}(z)$ and $\bold{R}(z)$ (shown here as the $\hbox{\sc DFT}$ and $\hbox{\sc IDFT}$ ).