ON THE 1D AND 2D ROGERS-RAMANUJAN CONTINUED FRACTIONS

被引：0
作者：
Antoniou, George E. [1 ]
Katsalis, Panagiota A. [2 ]
机构：
[1] Montclair State Univ, Dept Comp Sci, Montclair, NJ 07025 USA
[2] Montclair State Univ, Dept Math Sci, Montclair, NJ 07043 USA
来源：
JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS | 2011年 / 20卷 / 04期
关键词：
Rogers-Ramanujan; continued fractions; inversion; 1D/2D systems; multidimensional systems; INVERSION; FILTERS; CIRCUIT; DELAY;
D O I：
10.1142/S0218126611007475
中图分类号：
TP3 [计算技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
引用
收藏
页码：573 / 585
页数：13
相关论文
共 50 条
  • [1] Tasoev's continued fractions and Rogers-Ramanujan continued fractions
    Komatsu, T
    JOURNAL OF NUMBER THEORY, 2004, 109 (01) : 27 - 40
  • [2] On the divergence of the Rogers-Ramanujan continued fraction on the unit circle
    Bowman, D
    McLaughlin, J
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (08) : 3325 - 3347
  • [3] Continued Fractions and 2D Hurwitz Polynomials
    Jiří Gregor
    Multidimensional Systems and Signal Processing, 2002, 13 : 187 - 199
  • [4] Continued fractions and 2D Hurwitz polynomials
    Gregor, J
    MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, 2002, 13 (02) : 187 - 199
  • [5] 2-colored Rogers-Ramanujan partition identities
    Zadehdabbagh, Mohammad
    TURKISH JOURNAL OF MATHEMATICS, 2022, 46 (08) : 3352 - 3358
  • [6] 2-D Roger-Ramanujan Continued Fraction and Inversion
    Antoniou, George E.
    Katsalis, R. A.
    ISSCS 2009: INTERNATIONAL SYMPOSIUM ON SIGNALS, CIRCUITS AND SYSTEMS, VOLS 1 AND 2, PROCEEDINGS,, 2009, : 53 - 56
  • [7] 1D controllers for a class of 2D linear systems
    Benton, SE
    Rogers, E
    Owens, DH
    SYSTEM STRUCTURE AND CONTROL 1998 (SSC'98), VOLS 1 AND 2, 1998, : 305 - 310
  • [8] Asymmetric 1D and 2D tunneling induced grating in Quantum Dot system
    Abbas, Muqaddar
    Toheed, Kashaf
    Liu, Wenzhang
    Khadija
    Zhang, Yong-Chang
    Zhang, Pei
    OPTICS AND LASER TECHNOLOGY, 2024, 172
  • [9] The Effect of Inhomogeneous Magnetic Permeability on Magnetotelluric Responses: 1D and 2D Models
    Lozovsky, I. N.
    Varentsov, Iv M.
    IZVESTIYA-PHYSICS OF THE SOLID EARTH, 2022, 58 (05) : 615 - 625
  • [10] COMPARISON OF THE LENGTHS OF THE CONTINUED FRACTIONS OF ROOT-D AND 1/2(1+ROOT-D)
    WILLIAMS, KS
    BUCK, N
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 120 (04) : 995 - 1002
12345