Minimal state space realization for all-pole and all-zero lattice discrete 2D filters

Antoniou, Georgia

doi:10.1080/00207720210161740

Cited by 7 publications

(2 citation statements)

References 13 publications

(9 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By using the Z; I delay units and Z I Z� 1 basic lattice section, the proposed structure with the minimal number of delays is composed of the minimal number of basic lattice sections. Moreover, we consider the description of the proposed lattice structure by employing the well-known 2-D Roesser state space model [6] and the concepts presented in [7][8][9][10][11][12][13]. The dimension of the matrices of the model verifies the minimal state space realization of the proposed lattice structure.…”

Section: Introductionmentioning

confidence: 99%

General lattice structures of 2-D recursive digital filters

Lee

Yang

2011

2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS)

View full text Add to dashboard Cite

This paper presents a general lattice structure for the realization of two-dimensional (2-D) recursive digital filters. We employ two basic lattice sections to realize 2-D recursive digital filters with general coefficient support regions like a nonsymmetric half-plane (NSHP) support region. The matrix representations for the basic lattice sections are proposed and used to derive the transfer functions of the realized 2-D digital lattice filters. We use the Roesser state space model to verify the minimal realization of the proposed 2-D recursive digital lattice filter.I. I NTRODUCTIONThe design and implementation of one-dimensional (1-D) lattice filters have been reported in the literature [1-3]. I-D lattice filter structure exhibits the attractive advantages of low pass-band sensitivity and robustness to quantization error. The corresponding all-pole and all-pass lattice filters can be directly obtained from the I-D all-zero lattice structure. Additionally, I-D digital lattice filter structure requires lower computational cost than I-D direct form digital filter with similar design specifications. The minimal realization of a 2-D system presented by [4] has been widely concerned because it results in the least hardware requirement and less computational complexity. The minimal delay realization for a 2-D lattice structure has been presented in [5]. The cascaded 2-D digital lattice filter has the minimal number of delay elements 2n when n basic lattice sections are employed. The resulting 2-D digital lattice filter exhibits all-pass characteristics with a quarter-plane (Q P ) support region for its filter coefficients.In this paper, we consider the extension of 2-D lattice filters with more general support regions. By using the matrix representations of the basic lattice sections, we can directly derive the transfer functions of the proposed 2-D digital lattice filters including 2-D all-zero, 2-D all-pole, and 2-D all-pass filters. The proposed 2-D digital all-pass lattice filter has the coefficient support region with a nonsymmetric half plane.

show abstract

Section: Introductionmentioning

confidence: 99%

General lattice structures of 2-D recursive digital filters

Lee

Yang

2011

2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS)

View full text Add to dashboard Cite

show abstract

“…Different methods of solvability of 2D hybrid linear systems have been discussed in Kaczorek et al (2008) and the solution to singular 2D hybrids linear systems has been derived in Sajewski (2009). The realization problem for positive 2D hybrid systems have been addressed in Kaczorek (2002Kaczorek ( , 2008b, Sajewski andKaczorek (2009, 2010) and the minimal realization problem for all-pole (the transfer function with only poles) and all-zero (the transfer function with all zero poles) 2D systems has been addressed in Antoniou (2002) and Varoufakis et al (1987).…”

Section: Introductionmentioning

confidence: 99%

Positive Minimal Realization of Continuous-Discrete Linear Systems With All-Pole and All-Zero Transfer Function

Sajewski¹

2013

Acta Mechanica Et Automatica

View full text Add to dashboard Cite

The positive and minimal realization problem for continuous-discrete linear single-input and single-outputs (SISO) systems is formulated. Two special case of the continuous-discrete systems are given. Method based on the state variable diagram for finding a positive and minimal realization of a given proper transfer function is proposed. Sufficient conditions for the existence of a positive minimal realization of a given proper transfer function of all-pole and all-zero systems are established. Two procedures for computation of a positive minimal realization are proposed and illustrated by a numerical examples.

show abstract

2-D FIR discrete bidiagonal filters: Minimal circuit and state space realization

Antoniou

2009

2009 International Symposium on Signals, Circuits and Systems

View full text Add to dashboard Cite

In this paper 2-D circuit and state space realizations are presented for FIR bidiagonal discrete 2-D filters/systems. The proposed state space realization is based on the corresponding circuit implementation. For the state space realization the classical 2-D model of the Roesser type was used. The dimension of the state vector and the number of delay elements are minimal. Two examples are presented to illustrate the proposed results.

show abstract

Minimal state space realization for all-pole and all-zero lattice discrete 2D filters

Cited by 7 publications

References 13 publications

General lattice structures of 2-D recursive digital filters

General lattice structures of 2-D recursive digital filters

Positive Minimal Realization of Continuous-Discrete Linear Systems With All-Pole and All-Zero Transfer Function

2-D FIR discrete bidiagonal filters: Minimal circuit and state space realization

Contact Info

Product

Resources

About