Transfer Function and Error Probability of a Digital Magnetic Tape Recording System

Abstract

In spite of the complexities of the digital magnetic recording system, it has been discovered that the output of the system for the input of a unit step of current can be approximated by a Gaussian probability function A exp[−a(x−d)2]. The value “a” in A exp[−a(x−d)2] is a figure of merit of the system. This yields an analytic expression for the transfer function of the system. Experimental results correlate quite well with those based on this approximate transfer function. Using this transfer function, the output of the system for any Nonreturn to Zero recording method can be predicted. For example, the reduction in system output with increasing bit densities is established. In addition, when Gaussian noise is introduced into the system, the error probability is obtained. The effect of the input rise time to the output amplitude is discussed.