Hera memo #96: time correlations of eor signals for hera with vivaldi feeds

We compute fringe-rate filter specifications for HERA visibilities outfitted with Vivaldi feeds for the suppression of cross-coupling systematics and for coherent time averaging. We perform ensemble mock EoR simulations with a Vivaldi beam response to compute the power spectral density (PSD) of an EoR-like sky in the fringe-rate domain. Using this, we can set specifications for how aggressive a fringe-rate filter can be before it begins to attenuate a certain fraction of the EoR signal. Said another way, we can determine the lossiness of a time filter based on which fringe-rate modes it keeps and which it rejects. We perform these tests for a fiducial beam model, and for the first time explore how primary beam perturbations impact these results. For fiducial feed displacement perturbations less than 3 cm, we find that the perturbed beam has a negligible impact on the EoR time correlations in the visibilities.