questions about downsampling (blurring voxels)

[yhao-z]

The following pic is a screenshot of your excellent paper.

Questions

• what is the exact cut-off frequency of the HR signal and why this frequency has the relationship with $r_n$ of the LR signal?
• if i set ${r_n}/{r_a}=3$ and use $\sigma_s = 0.75 \times 3$, the Guassian kenel is [0.16, 0.17, 0.16], leading the voxel value in LR signal is lower than that of HR signal. Is it reasonable? It sames natural when the LR value is higher than HR.