A discussion of the necessity of automation of medical waveform analysis and of methods of performing this analysis is given as motivation for the project reported by this paper. This is followed by a short discussion of present methods which use either an analog or digital computer as a tool of analysis. Emphasis is placed on finding a better method of displaying the results of the analysis in some meaningful manner. The investigation of three proposed methods of using a large general-purpose digital computer to analyze medical waveforms and how each might give a useful display of the information contained in the waveform is reported. One method is selected for special discussion as to exactly how it might be implemented; reasons for selecting it over the other proposals are given. The selected method of analyzing medical waveforms (EEG in particular) and displaying the results involves performing a type of Fourier analysis on short sections of the waveform by using a special type of convolution and displaying the result on the cathode-ray display tube of the computer. Mathematical justification of the method of analysis is given. Such a system has been programmed and used on the Rice University Computer: actual procedures for use are discussed and special techniques which have been used are reported.