• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.315-328
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• 2021

A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in 𝑙²(ℤ_N) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.877-888
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• 2020

In this paper we discuss about the image of Gabor frame under a unitary operator and derive a sufficient condition under which a unitary operator from L²(ℝ) to 𝑙²(ℤ) maps Gabor frame in L²(ℝ) to a Gabor frame in 𝑙²(ℤ).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.321-334
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• 2022

We introduce a special class of structured frames having single generators in finite dimensional Hilbert spaces. We call them as pseudo B-Gabor like frames and present a characterisation of the frame operators associated with these frames. The concept of Gabor semi-frames is also introduced and some significant properties of the associated semi-frame operators are discussed.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.1-14
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• 2024

We seek for an invertible map B from L²(Γ) to L²(G), where G is a finite abelian group and Γ is the direct product of finite cyclic groups which is isomorphic to G, so that any Gabor frame in L²(G), is a generalized pseudo B-Gabor frame.

• 대한수학회지
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• 제51권5호
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• pp.897-918
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• 2014

This paper addresses multi-window Gabor frames with rational time-frequency product. Such issue was considered by Zibulski and Zeevi (Appl. Comput. Harmonic Anal. 4 (1997), 188-221) in terms of Zak transform matrix (so-called Zibuski-Zeevi matrix), and by many others. In this paper, we introduce of a new Zak transform matrix. It is different from Zibulski-Zeevi matrix, but more direct and convenient for our purpose. Using such Zak transform matrix we characterize rational time-frequency multi-window Gabor frames (Riesz bases and orthonormal bases), and Gabor duals for a Gabor frame. Some examples are also provided, which show that our Zak transform matrix method is efficient.

• 정보처리학회논문지B
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• 제9B권5호
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• pp.653-662
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• 2002

지문인식은 입력지문이 데이터베이스 내에 있는 특성인의 지문과 일치하는지 여부를 확인하는 것이다. 이를 위해 대형 지문 데이터베이스에서는 여러 가지 전처리 과정과 분류 및 매칭을 하고 소형 지문데이터 인식에서는 분류를 하지 않고 바로 매칭을 한다. 매칭 방법은 특징점 (단점, 분기점)에 기초한 매칭이 주를 이루고 있는데, 특징점에 기초한 매칭은 지문의 변환, 회전, 비선형 변형, 가짜 특징점 등이 발생하는 문제로 특징점 추출 및 특징점들 간의 정확한 매칭에 매우 복잡한 계산을 필요로 하고, 지문의 품질향상을 위해 많은 전처리 과정이 필요한 문제점이 있다. 본 논문에서는 이러한 문제점을 해결하기 위하여 지문인식에 특징점을 이용하지 않고, Gabor 필터에 지문을 통과시켜 얻은 지문의 융선에서 Gabor 특징값을 산출하여 이 특징값을 지문인식에 이용하는 간단한 새로운 방법을 제안하고 이 방법이 지문인식 실행에 가능성을 가지고 있음을 실험으로 증명하였다.

• 대한수학회보
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• 제50권6호
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• pp.1841-1846
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• 2013

In this paper we establish some new results on sums of Hilbert space frames and Riesz bases. We also provide a correction to some recently established results in [2].

• Journal of Communications and Networks
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• 제12권4호
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• pp.289-307
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• 2010

The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence-termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carry out model selection and recovery of sparse signals irrespective of the phases of the nonzero entries even if the number of nonzero entries scales almost linearly with the number of rows of the Alltop Gabor frame.

• 한국산학기술학회논문지
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• 제13권1호
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• pp.333-342
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• 2012

이 논문에서는 인간 청각 시스템에 기반한 모음 개시 지점 (VOP) 탐지 방법을 제시하였다. 이 방법을 통해 '지각의' 주파수 범위, 즉 선형 음향 주파수에서의 Mel Scale을 보여준 후 일련의 삼각 Mel-weighted Filter Bank를 만들어 인간의 청각 시스템에서 대역 필터링 기능을 시뮬레이션하였다. 이러한 비선형 임계 대역 Filter Bank는 데이터 차원수를 크게 감소시키고 비선형적으로 간격을 둔 Mel 스펙트럼에서 더욱 효과적으로 포먼트를 생성하기 위해 조파들의 영향을 제거해준다. Mel 스펙트럼의 첨두 에너지 합은 각 프레임의 특징으로 추출하고 에너지 진폭이 급격히 상승하기 시작할 때의 특성은 Gabor 윈도우를 사용하여 VOP로 탐지한다. 실험 결과를 통해서 다른 종류의 자음들과 연결된 12개의 모음들을 포함하는 한 단어 데이터베이스에 대한 제안된 방법의 평균 정확도는 단시간 에너지와 zero-crossing 비율에 기반을 둔 다른 모음 탐지 방법들보다 높은 72.73% 이상임을 확인하였다.

• Journal of the Korean Physical Society
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• 제73권9호
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• pp.1269-1278
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• 2018

Using the thawed Gaussian wave packets [E. J. Heller, J. Chem. Phys. 62, 1544 (1975)] and the adaptive reinitialization technique employing the frame operator [L. M. Andersson et al., J. Phys. A: Math. Gen. 35, 7787 (2002)], a trajectory-based Gaussian wave packet method is introduced that can be applied to scattering and time-dependent problems. This method does not require either the numerical multidimensional integrals for potential operators or the inversion of nearly-singular matrices representing the overlap of overcomplete Gaussian basis functions. We demonstrate a possibility that the method can be a promising candidate for the time-dependent $Schr{\ddot{o}}dinger$ equation solver by applying to tunneling, high-order harmonic generation, and above-threshold ionization problems in one-dimensional model systems. Although the efficiency of the method is confirmed in one-dimensional systems, it can be easily extended to higher dimensional systems.