Coordinates of the Earth pole over a period from 1962 to 1991 are repr
esented by a deterministic exponential model (method by Prony). Observ
ational data, obtained by services BIH and IERS are transformed (for m
odeling purposes) into a set of complex numbers. An exponential model
of the free polar motion with a period 403 +/- 14 days is obtained. Ma
thematical formulations for changes of the amplitude and the period ch
anges are developed. Values of the spectral energy density are compute
d for the transformed data. (Prony's spectrum).