State-space realization of 2-D systems via continued fraction expansion

Antoniou, Georgia; Varoufakis, S.J.; Paraskevopoulos, P.N.

doi:10.1109/tcs.1986.1086014

Cited by 36 publications

(8 citation statements)

References 13 publications

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“…Theorem 2: [4] Any circuit containing two bipolar junction transistors can possess no more than three operating points.…”

Section: On the Topology And Number Of Operating Points Of Mosfet Cirmentioning

confidence: 99%

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Generalized one-multiplier lattice discrete 2-D filters: minimal circuit and state-space realization

Antoniou

2001

IEEE Trans. Circuits Syst. I

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Abstract-A circuit realization is presented for generalized one-multiplier lattice discrete two-dimensional (2-D) filters. The proposed structure has a minimun mumber of delay elements and multipliers. Based on this circuit realization, the corresponding state-space realization-representation is derived. The dimension of the 2-D state-space vector is minimal and the corresponding transfer function is characterized by the all-pass property.

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“…Theorem 2: [4] Any circuit containing two bipolar junction transistors can possess no more than three operating points.…”

Section: On the Topology And Number Of Operating Points Of Mosfet Cirmentioning

confidence: 99%

“…In Section III , we present a brief outline of the proof of [4]. In Section IV, we show why this proof does not hold for MOSFETs and then present a simple two-transistor MOSFET circuit that possesses five operating points.…”

Section: On the Topology And Number Of Operating Points Of Mosfet Cirmentioning

confidence: 99%

Generalized one-multiplier lattice discrete 2-D filters: minimal circuit and state-space realization

Antoniou

2001

IEEE Trans. Circuits Syst. I

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“…The dimension of the resulting state-space realization will be minimal, i.e. m+ n, as in the work of Antoniou et al (1988).…”

Section: Inimality Of Realizationmentioning

confidence: 99%

Minimal circuit and state space realization of three-term separable denominator 2-D filters

Manikopoulos¹,

Mentzelopoulou²,

Antoniou³

1991

International Journal of Electronics

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A simple method is presented for the minimal state space realization of two dimensional(2-D)filters, with a three-term separable denominator (3TSD)made up of two 1-0 and one 2-D terms. The matrix A and the vectors b and e' of the state space model are derived explicitly from the coefficients of the initial transfer function. The circuit implementation for the 2-D 3TSD filters is provided, as well. The number of delay elements employed represents a significant reduction compared to earlier non-minimal realizations.

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“…In the realization theory area of two dimensional (2D) systems, CFE play an important role because it has been shown that in the case where a 2D transfer function is expanded into any type of CFE, it can be realized with a minimum number of delay elements. 5,6,8,9 Today the minimality is not related to thē nancial cost of the memory space, but to the execution speed of the¯lter.…”

Section: Introductionmentioning

confidence: 99%

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

Antoniou

Katsalis

2011

J CIRCUIT SYST COMP

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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.

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State-space realization of 2-D systems via continued fraction expansion

Cited by 36 publications

References 13 publications

Generalized one-multiplier lattice discrete 2-D filters: minimal circuit and state-space realization

Generalized one-multiplier lattice discrete 2-D filters: minimal circuit and state-space realization

Minimal circuit and state space realization of three-term separable denominator 2-D filters

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

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