  Given a frame in C^n which satisfies a form of the uncertainty principle (as
introduced by Candes and Tao), it is shown how to quickly convert the frame
representation of every vector into a more robust Kashin's representation whose
coefficients all have the smallest possible dynamic range O(1/\sqrt{n}). The
information tends to spread evenly among these coefficients. As a consequence,
Kashin's representations have a great power for reduction of errors in their
coefficients, including coefficient losses and distortions.
