• 대한수학회보
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• 제34권2호
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• pp.193-198
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• 1997

In order to research the logical system whose propositional value is given in a lattice, Y. Xu [4] proposed the concept of lattice implication algebras, and discussed their some properties in [3] and [4]. Y. Xu and K. Qin [5] introduced the notions of filter and implicative filter in a lattice implication algebra, and investigated their properties. In this paper, in the first place, we give an equivalent condition of a filter, and provide some equivalent conditions that a filter is an implicative filter in a lattice implication algebra. By using these results, we construct an extension property for implicative filter.

• 전자공학회논문지B
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• 제32B권11호
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• pp.1473-1480
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• 1995

When the LMS algorithm is employed in the transversal filter structure, the computational complexity can be kept reasonably low. However, if the impulse response to be estimated is very long or signals involved are highly correlated like a speech the convergence speed becomes slow. The lattice filter is an excellent alternative to improve convergence speed since the lattice structure inherently has the orthogonal property among the backward prediction errors, but at the expense of the excessive computational load. If the input signal to be used can be sufficiently well modeled as a .RHO.-th order autoregressive(AR) process, the reflection coefficients after the .RHO.- th stage will be close to zero. Then, instead of employing the full lattice structure, the joint lattice filter structure can be implemented in conjunction with the transversal filter structure after the .RHO.-th stage. We propose, in this paper, this new lattice/transversal joint structure, and we will call it the reduced lattice filter. Using the reduced lattice filter, we are now able to achieve the performance as good as that of the lattice filter, while maintaining the complexity as low as that of the transversal filter. The proposed filter is particularly useful for an acoustic echo canceller due to the highly correlatedness nature of speeches and the long and frequently changing echo paths.

• Journal of Mechanical Science and Technology
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• 제20권12호
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• pp.2043-2051
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• 2006

This paper considered identification of vibration characteristics of flexible structure with vector channel periodic lattice filter. We present an algorithm for AR coefficients for the vector-channel lattice filters, and characteristic equation and transfer function are derived from these coefficients. Vibration lattice filter is then constructed from the vector channel lattice filter, and performance of this vibration filter is tested with a test signal which is a combination of many sine waves to compare the performance of scalar and vector channel lattice. Also it is applied to the cantilever data to identify properties of the system, such as natural frequencies and damping ratios, to show its performance.

• 융합신호처리학회 학술대회논문집
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• 한국신호처리시스템학회 2001년도 하계 학술대회 논문집(KISPS SUMMER CONFERENCE 2001
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• pp.45-48
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• 2001

본 논문에서는 OFDM 시스템에 있어서 심블간 간섭을 일으키는 채널에 대해 lattice 필터를 사용한 등화기의 등화 특성을 검토하였다. Lattice 괼터를 사용한 등화기는 다른 등화기와 비교해서 단수마다의 직교화 효과에 의해, 탭 수가 작아도 수렴이 빠르고 등화 오차를 작게 할 수 있는 특징이 있다. 본 논문에서는 Lattice 필터를 사용한 등화기 필터 계수의 수렴성과 정적인 BER특성을 컴퓨터 시뮬레이션에 의해 해석하고 Transversal 필터 방식에 비해서 우수한 보상 방식인 것을 보인다.

• 전자공학회논문지B
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• 제29B권1호
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• pp.26-33
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• 1992

This paper presents lattice structure of bilinear filter and the conversion equations from lattice parameters to direct-form parameters. Billnear models are attractive for adaptive filtering applications because they can approximate a large class of nonlinear systems adequately, and usually with considerable parsimony in the number of coefficients required. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem and then uses multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The lattice filters perform a Gram-Schmidt orthogonalization of the input data and have very good easily extended to more general nonlinear output feedback structures.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.323-330
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• 2014

The notion of transitive filters is introduced in lattice implication algebras. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. The concept of absorbent filters is introduced and their properties are studied. A set of equivalent conditions is obtained for a filter to become an absorbent filter.

• 대한수학회보
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• 제35권1호
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• pp.53-61
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• 1998

We introduce the concepts of a positive implicative filter and an associative filter in a lattice implication algebra. We prove that (i) every positive implicative filter is an implicative filter, and (ii) every associative filter is a filter. We provide equivalent conditions for both a positive implicative filter and an associative filter.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.385-392
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• 2003

Using a fuzzy filter, a new congruence relation induced by the fuzzy filter is given in lattice implication algebras, and some of their properties are investigated.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.739-748
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• 2015

The notion of quasi-lattice implication algebras is a generalization of lattice implication algebras. In this paper, we give an optimized definition of quasi-lattice implication algebra and show that this algebra is a distributive lattice and that this algebra is a lattice implication algebra. Also, we define a congruence relation Φ_F induced by a filter F and show that every congruence relation on a quasi-lattice implication algebra is a congruence relation Φ_F induced by a filter F.

• 호남수학학술지
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• 제31권3호
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• pp.323-333
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• 2009

We introduce the concepts of a fuzzifying filter and a fuzzifying implicative filter in lattice implication algebras.