Effect of intra-channel baseline migration on the measured visibility and spatial power spectrum

The channel-to-channel migration of radio interferometric baselines for the same antenna separation causes a flat spectrum source that should have remained in the zeroth delay (line-of-sight) mode to become centered around a higher mode - the geometric delay for that particular antenna separation with a spread (spill-over) of the order of reciprocal bandwidth. While in principle an errorless gridding interpolation can remove inter-channel migration, intra-channel baseline migration exists due to the non-zero width (resolution) of the instrument's spectral channel arising from the finite-period integration in a DFT cycle. Here for the first time, we analyze this effect and quantify it using the case of a flat-spectrum point source. We find that the visibility undergoes an attenuation, the extent of which depends on the auto-correlation of the window function used for DFT and is more towards the lower-end of the band. This causes the spill-over of the delay mode to extend beyond the reciprocal bandwidth order.