This paper presents a procedure for using Hahn polynomials for the analysis and parameter estimation of linear discrete-time single-input/single-output systems described by difference equations. An advantage is gained through transforming a linear difference equation into a set of algebraic equations of the system parameters and the Hahn coefficients of the system variables. The key to the equation conversion is the derivation of a relation between the Hahn coefficients of a function and its time-shifted ones. Examples are provided to show the utilization of the procedure.