• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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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.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.11
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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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• v.20 no.12
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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.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2001.06a
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• pp.45-48
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• 2001

In this paper, the characteristic of the equalizer using Lattice filter was investigated in channel ISI (Inter-Symbol Interference) in OFDM (orthogonal frequency division multiplexing) system. The equalizer using lattice filter has more fast convergence and little equalization error characteristic in two number of tap by orthogonal effect of each tap than another equalizers. The filter coefficient convergency and static BER (bit error ratio) characteristic was analysed by computer simulation. In this paper, it is shown that the equalizer using lattice filter has the better performance than a equalizer which makes use of another equalization method.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.1
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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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• v.32 no.3_4
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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.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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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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• v.13 no.1_2
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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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• v.33 no.5_6
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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.

• Honam Mathematical Journal
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• v.31 no.3
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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.