X-ray Free Electron Lasers (FELs) have opened new avenues in photon science, providing coherent x-ray radiation pulses orders of magnitude brighter and shorter than previously possible. The emerging concept of “beam by design” in FEL accelerator physics aims for accurate manipulation of the electron beam to tailor spectral and temporal properties of radiation for specific experimental purposes, such as x-ray pump/x-ray probe and multiple wavelength experiments. A cost-efficient method to extract information on longitudinal Wigner distribution function of emitted FEL pulses is proposed. It requires only an ensemble of measured FEL spectra.