A new method of precise measurement of the revolution frequency distribution, F(f), in the muon storage ring, and hence muon momentum p, energy E, and equilibrium radius R distributions, has been developed and used in analyzing data in the muon g-2 experiment at Brookhaven National Laboratory. The method is partly based on the Fourier transform of the observed electron decay signal, which is known in this experiment only after some time t(s) after injection. It is shown that the standard Fourier transform would give a wrong frequency distribution even if the signal were known immediately after injection. Only the cosine Fourier transform with the property determined initial time t(0) (different for different detectors placed along the orbit) gives the correct frequency distribution in such a case. As for a later starting time, t(s) > t(0), a special procedure must be used to find t(0) and to compensate for the lack of information about the signal between t(0) and t(s). The new technique is highly accurate and radically different from that used by CERN in its muon g-2 experiment. (C) 2002 Elsevier Science B.V. All rights reserved.