Hi Hamid,
In the past, we have looked at particular transforms - for a selected initial condition and for particular pair of states (that are of interest to you). In my understanding, the ensemble/initial conditions average should have been done at the stage of the ACF calculations. Currently, Pyxiad only computes separate ACF for each initial condition. It would be good to implement the ensemble-averaging while computing the ACF. Then, there won't be the question about which spectrum to use or whether to average or not.
Best,
Alexey