  Redshifted 21 cm radiation originating from the cosmological distribution of
neutral hydrogen (HI) appears as a background radiation in low frequency radio
observations. The angular and frequency domain fluctuations in this radiation
carry information about cosmological structure formation. We propose that
correlations between visibilities measured at different baselines and
frequencies in radio-interferometric observations be used to quantify the
statistical properties of these fluctuations. This has an inherent advantage
over other statistical estimators in that it deals directly with the
visibilities which are the primary quantities measured in radio-interferometric
observations. Also, the visibility correlation has a very simple relation with
power spectrum. We present estimates of the expected signal for nearly the
entire post-recombination era, from the dark ages to the present epoch. The
epoch of reionization, where the HI has a patchy distribution, has a distinct
signature where the signal is determined by the size of the discrete ionized
regions. The signal at other epochs, where the HI follows the dark matter, is
determined largely by the power spectrum of dark matter fluctuations. The
signal is strongest for baselines where the antenna separations are within a
few hundred times the wavelength of observation, and an optimal strategy would
preferentially sample these baselines. In the frequency domain, for most
baselines the visibilities at two different frequencies are uncorrelated beyond
\Delta \nu ~ 1 MHz, a signature which in principle would allow the HI signal to
be easily distinguished from the continuum sources of contamination.
