  Observations of redshifted 21cm radiation from HI at high redshifts is an
important future probe of reionization. We consider the Multi-frequency Angular
Power Spectrum (MAPS) to quantify the statistics of the HI signal as a joint
function of the angular multipole l and frequency separation \Delta\nu. The
signal at two different frequencies is expected to get decorrelated as
\Delta\nu is increased, and quantifying this decorrelation is particularly
important in deciding the frequency resolution for future HI observations. This
is also expected to play a very crucial role in extracting the signal from
foregrounds as the signal is expected to decorrelate much faster than the
foregrounds (which are largely continuum sources) with increasing \Delta\nu. In
this paper we develop formulae relating the MAPS to different components of the
three dimensional HI power spectrum taking into account HI peculiar velocities.
We show that the flat-sky approximation provides a very good representation
over the angular scales of interest, and a final expression which is very
simple to calculate and interpret. We present results considering two models
for the HI distribution, namely, (i) DM: where the HI traces the dark matter
and (ii) PR: where the effects of patchy reionization are incorporated through
two parameters. We find that while the DM signal is largely featureless, the PR
signal peaks at the angular scales of the individual bubbles, and the signal is
considerably enhanced for large bubble size. For most cases of interest at l
\sim 100 the signal is uncorrelated beyond \Delta\nu \sim 1 MHz or even less,
whereas it occurs around \sim 0.1 MHz at l \sim 10^3. The \Delta\nu dependence
also carries an imprint of the bubble size and the bias, and is expected to be
an important probe of the reionization scenario (abridged).
