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It is well known that the pulse height distribution from a scintillation spectrometer may differ considerably from the spectrum of the incident radiation because the radiation may interact in several different ways with the crystal. Statistical variations in the pulses produce an additional distortion. These facts greatly complicate the quantitative analysis of continuous spectra or discrete spectra with more than a few different energies. Although it is not possible to calculate the exact "unscrambled spectrum," it is possible to obtain a "best estimate" of the incident spectrum and to assign meaningful errors to the result. A clarifying point of view based on Fourier techniques is introduced. Methods for numerical calculation are then described.