In Dr.Joel's book and the paper titled "Gating Effects in Time Domain Transforms", the the following is given.

"The VNA time domain compensates for this roll-off through a post-gate renormalization. The post-gate renormalization is a function determined by creating a frequency response that is unit magnitude. A pre-gate window is applied to this unit-response that is the same as the pre-transform window applied to the normal frequency response data.................."

I can't undersatand why the pre-gate window is used. I thought that the final normalizing frequency response could be caculated without the pre-gate window.

look forward the reply!

The goal of renormalization is to correct for mathematical gating loss. Thus a known signal is applied to the gating process and the difference between the gated result and the known signal is the renormalization value. As such the known signal needs to go through the same processing steps as an unknown measured signal.