  Detection of 21~cm emission of HI from the epoch of reionization, at
redshifts z>6, is limited primarily by foreground emission. We investigate the
signatures of wide-field measurements and an all-sky foreground model using the
delay spectrum technique that maps the measurements to foreground object
locations through signal delays between antenna pairs. We demonstrate
interferometric measurements are inherently sensitive to all scales, including
the largest angular scales, owing to the nature of wide-field measurements.
These wide-field effects are generic to all observations but antenna shapes
impact their amplitudes substantially. A dish-shaped antenna yields the most
desirable features from a foreground contamination viewpoint, relative to a
dipole or a phased array. Comparing data from recent Murchison Widefield Array
observations, we demonstrate that the foreground signatures that have the
largest impact on the HI signal arise from power received far away from the
primary field of view. We identify diffuse emission near the horizon as a
significant contributing factor, even on wide antenna spacings that usually
represent structures on small scales. For signals entering through the primary
field of view, compact emission dominates the foreground contamination. These
two mechanisms imprint a characteristic "pitchfork" signature on the
"foreground wedge" in Fourier delay space. Based on these results, we propose
that selective down-weighting of data based on antenna spacing and time can
mitigate foreground contamination substantially by a factor ~100 with
negligible loss of sensitivity.
