Exponential series statistical modeling of track misregistration in magnetic storage channels

The authors apply the analytic method of exponential series expansion to empirical frequency distributions obtained from measurements of track misregistration (TMR) phenomena in magnetic storage head-disk-assembly (HDA) devices. Analytical expressions that represent the deviation of the empirical TMR frequency distributions from the Gaussian distribution are computed. The latter becomes the first term in a series of orthogonal functions with coefficients determined by the moments of the empirical distribution. This allows for adequately matching the tails of the empirical distributions where the Gaussian fit is poor and where HDA performance predictions are most interesting. The authors describe the computation of the exponential series coefficients for TMR empirical frequency distributions as well as the algebraic composition of these coefficients used to obtain models for the combined effect of several TMR phenomena