An unfolding algorithm using parabolic B-splines to smoothly reconstruct the soft x-ray spectra from the measurements of a filtered x-ray diode array is proposed. This array has been fabricated for the study of the soft x ray emitted by Z-pinch plasma. Unfolding results show that for the simulated noise-free blackbody spectra with temperature ranging from 20 to 250 eV, both the spectra and the total power are accurately recovered. Typical experimental waveforms along with the unfolded spectra and total power of x rays are presented. Possible defects due to the adoption of parabolic B-splines instead of conventionally used histograms are discussed.