A systematic theoretical study of a saturation type of recordingand reproduction in digital magnetic tape systems was undertakenso that the details of these processes could be more clearly understood.The dependence of tape magnetization and of output signalpulse width and amplitude on the major system parameters hasbeen investigated and determined. These parameters are themagnetic field distribution of the recording head, write currentwaveform, tape thickness and hysteresis characteristics, head-to-tapespacing, reading gap length, and bit density. A portion ofthis study is presented here, concerning the extension of thesinusoidal theory to include the reproduction of signals resultingfrom saturation recording. This is done by a Fourier analysis ofthe tape magnetization and a term-by-term summation of harmonicresponses to obtain the resultant signal. The results showwhy high writing field gradients, high tapeB-H“squareness,”and thin tapes are needed for high-density recording. They indicatepossible reasons for emf pulse peak position asymmetries duringreadback. Two examples of output calculations are included. Oneshows the signal amplitude and pulse width vs bit density, comparedwith experimental measurements. The other presents thefield distribution above the magnetized tape, indicating the influenceof the presence of the read head.