A Differential and Autoregressive Formulation of A Linear Regression Model for Fitting Spectroscopic Sinc Function Data

Abstract

This paper gives an account of fitting a sinc model to the interference fringe data. Fitting a sinc model can be considered as a nonlinear regression problem solvable by standard iterative methods. This paper sheds some light on how this nonlinear problem can be reformulated as simple linear regression problem solvable in a closed-form without the need for iterative methods. The adopted approach starts by converting this nonlinear regression problem to a linear regression problem by representing the sinc model in its differential (DFM) and autoregressive (ARM) form. From this new formulation, the fitting problem reduces to a simple linear regression problem that is solvable by ordinary least squares. The success of this linear regression problem reformulation is demonstrated with some hypothetical data set data and comments are made on its sensitivity to both noise and data sampling rate. Lastly an interference fringe data from a 633 nm laser beam is used for fitting the sinc model and the results are satisfactory.