  In recent years X-ray Free Electron Lasers (XFELs) proved to be unmatched
sources of ultrashort pulses of spatially coherent quasimonochromatic X-ray
radiation. Diagnostics of XFEL emission properties, in particular pulse
duration, spectrum and temporal profile is extremely important in order to
analyze the experimental results. In this paper we propose a cost-effective
method to examine these properties of Self-Amplified Spontaneous Emission
(SASE) pulses. It only requires an ensemble of measured SASE spectra and
provides the temporal autocorrelation of the ensemble-averaged Wigner
distribution of SASE FEL pulses.
