Exponential series statistical modeling of track misregistration in magnetic storage channels

The ability to predict off-track performance and to assess the efficiency or signal processing and coding schemes depends on having a good analytic representation of the track misregistration (TMR) noise. We apply the analytical method or exponential series expansion to empirical frequency distributions obtained from measurement of this noise in magnetic storage head-disk-assembly (HDA) devices. Traditionally, the analytic model used in the industry has been Gaussian distribution. The use of such a model reduces a huge mass or measurement data to a single number, the dispersion or variance, provided the origin is shifted to the mean value. The argument that is used to justify this procedure is the central limit theorem, which is an asymptotic result. Instead we compute analytic expressions that represent the deviation or the TMR frequency distributions from the Gaussian. The latter becomes the first term in a series of orthogonal functions with coefficients determined by the moments of the empirical distributions. This allows for adequately matching the tails or these distributions where the Gaussian fit is poor and there HDA performance predictions are most interesting.