DIGITAL RECORDING THEORY

Magnetic recording was initially applied to the recording and reproduction of sound, and the early theoretical treatments on the subject were concerned with sinusoidal magnetization distributions. The classic papers of Wallace and Westmijze 2 provided an adequate treatment of the theory of sinusoidal recording, which formed the foundation for many of the subsequent theoretical treatments of sinusoidal as well as square wave recording. It was recognized that the resolution and signal output of a recording channel are limited by a number of losses which can be separated into frequency-dependent and wavelength-dependent losses. The frequency-dependent losses comprise the eddy current and permeability variation effects in the recording transducers and media that are conducting or supported by conducting substrates, and the associated inductance and write current rise time variations with frequency. The wavelength-dependent losses relate to the geometrical aspects of the recording system-transducer gaps, transducer-to-medium spacing, recording medium thickness-and also to the demagnetization effects in the recording medium. In the early recording applications, it was the playback transducer that dominated and limited the response of the recording channel, and the first theoretical studies *, were primarily concerned with the treatment of the wavelengthdependent losses connected with the replay gap, spacing, and the effective spacing due to the thickness of the medium. A simple treatment of demagnetization effects in the medium was also provided by Westmijze * for a sinusoidal magnetization pattern, by calculating a demagnetizing factor and applying it t o the hysteresis loop of the medium to obtain a new magnetization distribution. Since the playback process is essentially linear, the reciprocity theorem can be used to calculate the output voltage waveform by convolving the medium magnetization with the head field function, and the theory of saturation magnetic recording was initially developed on this basis3-0 (demagnetization effects in the recording medium were either altogether disregarded, or a linear or an arctangent magnetization transition of arbitrary or indeterminate extent was assumed). For an assumed magnetization distribution in the recording medium, one can calculate the playback voltage waveform by using the method of images instead of employing the reciprocity theorem (and get essentially the same result!). This method was used by Miyata and Hartel ' (following a similar approach by Wallace for sinusoidal recording). They assumed an arctangent function for the magnetization transition with an adjustable parameter which controls the initial slope of the function, and obtained an analytical expression for the pulse waveform read back by an ideal transducer. Chapman obtained