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In this paper the classical and generalized numerical Rogers-Ramanujan 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 filters in one and two dimensions signal processing. The simplicity and efficiency of the presented algorithms are illustrated by step-by-step examples. [ABSTRACT FROM AUTHOR]

In this paper, the discrete Fourier transform is used to determine the coefficients of a transfer function of a new generalized two-dimensional system of second-order: Ex(i1 + 2, i2 + 2) = A0x(i1 + 1, i2 + 1) + A1x(i1 + 1, i2) + A2x(i1, i2 + 1). The algorithm is straightforward and has been implemented using the software package Matlab™. A step-by-step example illustrating the application of the algorithm is presented. [ABSTRACT FROM AUTHOR]

In this paper, the one-dimensional Gray–Markel lattice-ladder discrete filter structure is extended to two dimensions (2D). The proposed 2D circuit implementation has minimal number of unit delays. Based on this circuit implementation the corresponding 2D state space realization is derived. The matrices A, b, c′ and the scalar d of the 2D state space model are presented in generalized closed form, having minimal dimension. [ABSTRACT FROM AUTHOR]