Applications of Fourier transforms in digital magnetic recording theory

In this paper we present a unified treatment of many problems in digital pulse recording. The physics appropriate to each problem is characterized by a reciprocal-space transfer function, which may be abstracted from published studies of sine wave recording. Over twenty-five transfer functions are given in appendices. Given the transfer functions, an inverse Fourier transformation completes each problem. The fields, fluxes, and output voltage due to an arctangent magnetization profile in a tape of unit permeability are derived. A closely related case, that of a linear ramp magnetization, is treated briefly. A step function magnetization is considered for a tape of nonunit permeability in which, dependent upon the boundary conditions, demagnetization and remagnetization occur. Extensions of the theory of multitransition waveforms are undertaken, yielding the spectra of both regular and random sequences.