On the 1d and 2d Rogers–ramanujan Continued Fractions

Abstract

In this paper the classical and generalized numerical RogersÀRamanujan continued fractions are extended to a polynomial continued fraction in one and two dimensions. Using the new continued fractions, the fundamental recurrence formulas and a fast algorithm, based on matrix formulations, are given for the computation of their transfer functions. The presented matrix formulations can provide a new perspective to the analysis and design of Ladder-continued fraction¯lters in one and two dimensions signal processing. The simplicity and e±ciency of the presented algorithms are illustrated by step-by-step examples.