  We propose an all-digital telescope for 21 cm tomography, which combines key
advantages of both single dishes and interferometers. The electric field is
digitized by antennas on a rectangular grid, after which a series of Fast
Fourier Transforms recovers simultaneous multifrequency images of up to half
the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has
now reached about 1 GHz, and will likely continue doubling every couple of
years. The main advantages over a single dish telescope are cost and orders of
magnitude larger field-of-view, translating into dramatically better
sensitivity for large-area surveys. The key advantages over traditional
interferometers are cost (the correlator computational cost for an N-element
array scales as N log N rather than N^2) and a compact synthesized beam. We
argue that 21 cm tomography could be an ideal first application of a very large
Fast Fourier Transform Telescope, which would provide both massive sensitivity
improvements per dollar and mitigate the off-beam point source foreground
problem with its clean beam. Another potentially interesting application is
cosmic microwave background polarization.
