Deriving a linear model for passively acquired bio-potentials using sample ACF

In this paper, a closed form of the sample autocor-relation function (ACF) of a deterministic as well as a stochastic straight line have been derived and the corresponding 1
^st
zero crossing lag values of the sample ACF have been identified. It has been observed that for a deterministic straight line, the zero crossing lag value is independent of the slope and the intercept, but depends on the number of data samples. However, for the straight line corrupted with Gaussian noise, this is dependent on the slope as well as the number of data samples. It has also been observed that the change of noise interaction affects the 1
^st
zero crossing lag value accordingly. This finding has been used to develop an algorithm to identify signals that follow a linear trend with a stated limit on the associated noise, henceforth referred to as quasilinear signals. This algorithm has been applied to sort bio-potentials that are passively acquired from the fingers of human subjects at rest, since their time-plots seem to change almost linearly over a short duration of 2 minutes. All the acquired signals have been fitted with best-fit straight lines and the residuals of the two classes of signals have been compared. It is observed that, in general, the quasilinear signals identified using the proposed algorithm have smaller residuals.