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.     

Signal equalization in digital magnetic recording

The signal applied to the head in the writing process undergoes changes and distortions of various sources. Equalization must be applied to the read signal to help restore the input waveshape. The object is to improve timing accuracy which ultimately allows the use of increased bit density. An equalization method is presented in which amplitude and phase are controlled separately. The phase equalizer is adjustable, compensating for waveshape asymmetry. The networks are extremely simple and not sensitive to component tolerances. In continuous waveshape codes, such as phase recording or double frequency recording, the system is capable of compensating for considerable variations in the spacial parameters of recording. The equalization can also be used in nonreturn to zero (NRZ) code, where the ability to restore symmetry can be used to great advantage in eliminating errors.     

Optimum media thickness for digital recording

Thinner media yield narrower output pulses, and in many low density digital recorders this leads to better performance. In high density applications, however, the signal-to-noise ratio (SNR) is of greater importance than pulsewidth. The SNR depends on both the write process and the origin of the dominant noises. Several types of media noise, reproduce head, and electronic noises are discussed. A method of determining the media thickness yielding the highest SNR is outlined. The results are dependent upon the noise sources and we conclude that a generally valid rule cannot be given. In some cases a thicker medium may be preferable to a thinner one and vice versa.     

Output waveforms in the replay process in digital magneticrecording

The output voltage waveforms expected when replaying with various head structures from media magnetized in arbitrary directions are predicted. Expressions are given in useful closed forms for the outputs in isolated and pulse crowded circumstances. Output waveforms are shown for a range of orientations of the recorded magnetization to reveal aspects of pulse symmetry and their effects on “roll-off” curves     

Representation of a digital magnetic recording channel

A representation or model of a digital magnetic recording channel which has value both as an expression of the transfer characteristics of the channel and as a tool for use in the design and development of digital coding techniques for that channel is presented     

A computer simulation of unbiased digital recording

This simulation is intended for use at low, intermediate, and high bit densities. While simpler algorithms can be found for use with either very low bit densities only, or with very high bit densities only, they lack the generality needed for this purpose. The simulation is composed of three distinct sequential computations. First, using a noninteracting particle idealizedM_{r}-Hmodel and the arctangent head field formula, the tape magnetization is computed at 40 points per bit length in each of 5 laminae. Second, this magnetization is averaged throughout the tape thickness and harmonically analyzed. Finally, each harmonic component is weighted according to a demagnetizing-remagnetizing factor given previously, and the final output voltage waveform is computed. Linearity and superposition are thus assumed for all processes following the obviously nonlinear record mechanism. Computed outputs are compared with experimental results for both single transition and multiple transition inputs. The widths of computed and measured isolated output pulses differ by no more than 10 percent, without the adoption of physically unreasonable parameters. Output signals were computed for multiple transition inputs up to 20 000 flux reversals per inch (fr/in), and these compare well with experimental results up to 15000 fr/in.     

Sputtered multilayer films for digital magnetic recording

Layered films of cobalt over chromium deposited by dc sputtering onto heated substrates exhibit magnetic properties suitable for digital saturation recording. A cobalt layer of a few tens of nanometers thickness deposited over a chromium layer of several hundred nanometers has coercivity between 1100 and 300 Oe and remanence-thickness product between 0.014 and 0.07 G.cm with squareness between 0.7 and 0.95. Additional alternate layers of chromium and cobalt can increase remanent flux without reduction of coercivity. Magnetic properties can be tailored to specific needs by varying layer thicknesses.     

Thin metallic films for high-density digital recording

Three different methods, electrodeposition, autocatalytic deposition, and vacuum deposition, by which thin metal films may be made are described. They have a combination of magnetic characteristics which should make them well suited to the purpose of high density recording. It is concluded that the factors which are primarily responsible for the superior recording performance of these films when compared with the conventional particulate coatings are their thinness and their high coercivity.     

Power spectra of channel codes for digital magnetic recording

The power spectral density (PSD) is the average power per unit frequency of encoded random data transmitted over a perfect channel. The one-sided PSDs of a number of channel codes of recent interest in digital magnetic recording are calculated from codeword dictionaries and state diagrams. Given here are:     

A theory of digital magnetic recording on metallic films

A theory is presented predicting the performance of thin magnetic tape as a digital storage medium. The NRZ recording properties are discussed with reference to the properties of both the tape and the replay head. Expressions are derived relating the isolated pulse width, the output voltage, and the packing density to the coercivity and thickness of the tape, the head gap length, and the head-to-tape separation. The theoretical predictions are then compared with experimental results measured over a wide range of head and tape properties. The agreement obtained is excellent.     

Characteristics of the readback signal in digital magnetic recording

A theoretical treatment for the readback process in digital magnetic recording is presented. Three major factors, namely, the medium constantswhich defines the extent of the surface charge density, the head-to-medium spacingd, and the read head gap2 g,are taken into consideration. A general solution giving the characteristics of pulse readback signal is shown as a function ofs,dandg. Both amplitude and pulse width of the readback signal are arranged as a product of the medium loss, spacing loss, and gap loss, making it easy to describe the influence of each factor separately. The final value of the amplitude and the pulse width is proportional to that of the recorded surface charge density. Spacing loss simply depends on the ratio ofd/s; gap loss depends on the ratio ofg/(s + d). Theoretical results are compared with experiments which show good agreement for a wide combination ofs,d, andg.     

Determination of large-scale out-of-plane displacements in digital Fourier holography

A novel approach for the determination of large-scale out-of-plane displacements from digital Fourier holograms is presented. The proposed method is invariant to lateral object shifts. It is based on the determination of the scaling of the reconstructed image that occurs when the recording distance is changed. For a precise determination of the scaling factor, we utilize the Mellin transform. After the discussion of mathematical and computational issues, experimental results are presented to verify the theoretical considerations. The results show that displacements of at least up to 8.4% from the initial recording distance can be detected with this approach. The displacements could be determined with a deviation of typically less than 1.0% from the set values.