Delay Spectrum with Phase-Tracking Arrays: Extracting the HI power spectrum from the Epoch of Reionization

The Detection of redshifted 21 cm emission from the epoch of reionization (EoR) is a challenging task owing to strong foregrounds that dominate the signal. In this paper, we propose a general method, based on the delay spectrum approach, to extract HI power spectra that is applicable to tracking observations using an imaging radio interferometer (Delay Spectrum with Imaging Arrays (DSIA)). Our method is based on modelling the HI signal taking into account the impact of wide field effects such as the $w$-term which are then used as appropriate weights in cross-correlating the measured visibilities. Our method is applicable to any radio interferometer that tracks a phase center and could be utilized for arrays such as MWA, LOFAR, GMRT, PAPER and HERA. In the literature the delay spectrum approach has been implemented for near-redundant baselines using drift scan observations. In this paper we explore the scheme for non-redundant tracking arrays, and this is the first application of delay spectrum methodology to such data to extract the HI signal. We analyze 3 hours of MWA tracking data on the EoR1 field. We present both 2-dimensional ($k_\parallel,k_\perp$) and 1-dimensional (k) power spectra from the analysis. Our results are in agreement with the findings of other pipelines developed to analyse the MWA EoR data.