  Following Cand\`es, Romberg and Tao (IEEE Transactions on Information Theory
20,2 (2006) 489-509) a signal is represented as a function x defined on the
cyclic group G = Z / NZ, and assuming that it is carried by a set S consisting
of T points, we want to reconstruct x using only a small set W of frequencies.
The procedure is the minimal extrapolation of the restriction of the Fourier
transform of x to W in the Wiener algebra of the dual of G , and the condition
for that to work is a relation between x and W. The note gives conditions on S
and W, and conditions on T and W for it to work, and uses random choices in
another way than Cand\`es, Romberg and Tao in order to get new results. The
idempotent whose Fourier transform is the indicator function of W plays a
central role.
