We present a detailed analysis of post-correlation (PC) beamforming (i.e., beamforming which involves only phased sums of the correlation of the voltages of different antennas in an array), and compare it with the traditionally used incoherent and phased beamforming techniques. Using data from the GMRT we show that PC beam formation results in a manyfold increase in the signal-to-noise for periodic signals from pulsars and reductions, of several orders of magnitude, in the number of false triggers from single-pulse events like fast radio bursts (FRBs). This difference arises primarily because the PC beam contains less red noise, as well as less radio frequency interference. The PC beam can also be more easily calibrated than the incoherent or phased array beams. We also discuss two different modes of PC beam formation: (1) by subtracting the incoherent beam from the coherent beam and (2) by phased addition of the visibilities. The computational costs for both these beam formation techniques, as well as their suitability for studies of pulsars and FRBs, are discussed. The techniques discussed here should be of interest for all upcoming surveys with interferometric arrays. Finally, we describe a time-domain survey with the GMRT using the PC beam formation as a case study. We find that PC beamforming will improve the current GMRT time-domain survey sensitivity by ~2 times for pulsars with periods of few hundreds of milliseconds and by many-folds for even slower pulsars, making it one of the most sensitive surveys for pulsars and FRBs at low and mid radio frequencies.
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