Stability and synthesis of two-dimensional recursive filters

Shanks, John L.; Treitel, Sven; Justice, James H.

doi:10.1109/tau.1972.1162358

Cited by 316 publications

(70 citation statements)

References 12 publications

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“…This method is related to that proposed by Shanks et al (1972) for the design of 2-D infinite impulse response filters. Shanks' method, however, is formulated in the space-time domain (as opposed to the frequency domain), and its algorithmic implementation is different.…”

Section: Substitution Of This Constraint Into Equation (3-6) Results mentioning

confidence: 99%

Two-Dimensional Processing for Radar Systems

Roman¹,

Davis²,

Zhang³

1997

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Section: Substitution Of This Constraint Into Equation (3-6) Results mentioning

confidence: 99%

Two-Dimensional Processing for Radar Systems

Roman¹,

Davis²,

Zhang³

1997

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“…Instead of working with a transfer function, which depends on one independent variable, they looked at polynomial functions of 2 and more generally variables. The notion of stability has also been investigated in terms of BIBO stability (bounded input bounded output) [1]. This led to the famous stability criterion which roughly states that the transfer function is BIBO stable for systems devoid of poles outside the stability region.…”

Section: A Historical Contextmentioning

confidence: 99%

Lyapunov Theory for 2-D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability

Yeganefar

Ghamgui

et al. 2013

IEEE Trans. Automat. Contr.

124

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Abstract-This technical note deals with a general class of discrete 2-D possibly nonlinear systems based on the Roesser model. We first motivate the introduction of Lyapunov type definitions of asymptotic and exponential stability. This will allow us to introduce and discuss several particularities that cannot be found in 1-D systems. Once this background has been carefully designed, we develop different Lyapunov theorems in order to check asymptotic and exponential stability of nonlinear 2-D systems. Finally we propose the first converse Lyapunov theorem in the case of exponential stability.

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“…2(a)). Weighted low rank approximations [15,16] using singular value decomposition (SVD) to find the desired frequency responses for the 1-D subfilters is the most common technique. The parallel branches corresponding to the largest singular values then forms the implemented filter as in Eq.…”

Section: T T T T T T T T T T T T T T T Tmentioning

confidence: 99%

A Graph Representation of Filter Networks

2005

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Abstract.Filter networks, i.e. decomposition of a filter set into a layered structure of sparse subfilters has been proven successful for e.g. efficient convolution using finite impulse response filters. The efficiency is due to the significantly reduced number of multiplications and additions per data sample that is required. The computational gain is dependent on the choice of network structure and the graph representation compactly incorporates the network structure in the design objectives. Consequently the graph representation forms a framework for searching the optimal network structure. It also removes the requirement of a layered structure, at the cost of a less compact representation.

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Stability and synthesis of two-dimensional recursive filters

Cited by 316 publications

References 12 publications

Two-Dimensional Processing for Radar Systems

Two-Dimensional Processing for Radar Systems

Lyapunov Theory for 2-D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability

A Graph Representation of Filter Networks

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