• Title/Summary/Keyword: Generalized Gaussian

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A TRANSLATION THEOREM FOR THE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE

  • Chang, Seung Jun;Choi, Jae Gil;Ko, Ae Young
    • Journal of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.991-1017
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    • 2016
  • In this paper we define a generalized analytic Fourier-Feynman transform associated with Gaussian process on the function space $C_{a,b}[0,T]$. We establish the existence of the generalized analytic Fourier-Feynman transform for certain bounded functionals on $C_{a,b}[0,T]$. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.

An Adaptive Noise Removal Method Using Local Statistics and Generalized Gaussian Filter (국부 통계 특성 및 일반화된 Gaussian 필터를 이용한 적응 노이즈 제거 방식)

  • Song, Won-Seon;Nguyen, Tuan-Anh;Hong, Min-Cheol
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.35 no.1C
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    • pp.17-23
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    • 2010
  • In this paper, we present an adaptive noise removal method using local statistics and generalized Gaussian filter. we propose a generalized Gaussian filter for removing noise effectively and detecting noise adaptively using local statistics based human visual system. The simulation results show the objective and subjective capabilities of the proposed algorithm.

A REPRESENTATION FOR AN INVERSE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE

  • Choi, Jae Gil
    • The Pure and Applied Mathematics
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    • v.28 no.4
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    • pp.281-296
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    • 2021
  • In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space Ca,b[0, T]. The function space Ca,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶk of exponential-type functionals. We then establish that a composition of the Ƶk-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

Signal Subspace-based Voice Activity Detection Using Generalized Gaussian Distribution (일반화된 가우시안 분포를 이용한 신호 준공간 기반의 음성검출기법)

  • Um, Yong-Sub;Chang, Joon-Hyuk;Kim, Dong Kook
    • The Journal of the Acoustical Society of Korea
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    • v.32 no.2
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    • pp.131-137
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    • 2013
  • In this paper we propose an improved voice activity detection (VAD) algorithm using statistical models in the signal subspace domain. A uncorrelated signal subspace is generated using embedded prewhitening technique and the statistical characteristics of the noisy speech and noise are investigated in this domain. According to the characteristics of the signals in the signal subspace, a new statistical VAD method using GGD (Generalized Gaussian Distribution) is proposed. Experimental results show that the proposed GGD-based approach outperforms the Gaussian-based signal subspace method at 0-15 dB SNR simulation conditions.

Simple Detection Based on Soft-Limiting for Binary Transmission in a Mixture of Generalized Normal-Laplace Distributed Noise and Gaussian Noise

  • Kim, Sang-Choon
    • ETRI Journal
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    • v.33 no.6
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    • pp.949-952
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    • 2011
  • In this letter, a simplified suboptimum receiver based on soft-limiting for the detection of binary antipodal signals in non-Gaussian noise modeled as a generalized normal-Laplace (GNL) distribution combined with Gaussian noise is presented. The suboptimum receiver has low computational complexity. Furthermore, when the number of diversity branches is small, its performance is very close to that of the Neyman-Pearson optimum receiver based on the probability density function obtained by the Fourier inversion of the characteristic function of the GNL-plus-Gaussian distribution.

Review of Spatial Linear Mixed Models for Non-Gaussian Outcomes (공간적 상관관계가 존재하는 이산형 자료를 위한 일반화된 공간선형 모형 개관)

  • Park, Jincheol
    • The Korean Journal of Applied Statistics
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    • v.28 no.2
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    • pp.353-360
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    • 2015
  • Various statistical models have been proposed over the last decade for spatially correlated Gaussian outcomes. The spatial linear mixed model (SLMM), which incorporates a spatial effect as a random component to the linear model, is the one of the most widely used approaches in various application contexts. Employing link functions, SLMM can be naturally extended to spatial generalized linear mixed model for non-Gaussian outcomes (SGLMM). We review popular SGLMMs on non-Gaussian spatial outcomes and demonstrate their applications with available public data.

Asymptotic Gaussian Structures in a Critical Generalized Curie-Wiss Mean Field Model : Large Deviation Approach

  • Kim, Chi-Yong;Jeon, Jong-Woo
    • Journal of the Korean Statistical Society
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    • v.25 no.4
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    • pp.515-527
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    • 1996
  • It has been known for mean field models that the limiting distribution reflecting the asymptotic behavior of the system is non-Gaussian at the critical state. Recently, however, Papangelow showed for the critical Curie-Weiss mean field model that there exist Gaussian structures in the asymptotic behavior of the total magnetization. We construct Gaussian structures existing in the internal fluctuation of the system for the critical case of a generalized Curie-Weiss mean field model.

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SURFACES FOLIATED BY ELLIPSES WITH CONSTANT GAUSSIAN CURVATURE IN EUCLIDEAN 3-SPACE

  • Ali, Ahmed T.;Hamdoon, Fathi M.
    • Korean Journal of Mathematics
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    • v.25 no.4
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    • pp.537-554
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    • 2017
  • In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.

The Waveform Model of Laser Altimeter System with Flattened Gaussian Laser

  • Ma, Yue;Wang, Mingwei;Yang, Fanlin;Li, Song
    • Journal of the Optical Society of Korea
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    • v.19 no.4
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    • pp.363-370
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    • 2015
  • The current waveform model of a laser altimeter is based on a Gaussian laser beam of fundamental mode, while the flattened Gaussian beam has many advantages such as nearly constant energy distribution on the center of the cross-section. Following the theory of the flattened Gaussian beam and the waveform theory of the laser altimeter, some of the primary parameters of the received waveform were derived, and a laser altimetry waveform simulator and waveform processing software were programmed and improved under the circumstance of a flattened Gaussian beam. The result showed that the bias between theoretical and simulated waveforms was less than 3% for every order mode, the waveform width and range error would increase as target slope or order number rose. Under higher order mode, the shapes of the received waveforms were no longer Gaussian, and could be fitted more precisely as a generalized Gaussian function with power bigger than 2. The flattened beam got much better performance for a multi-surface target, especially when the small surface is far from the center of the laser footprint. This article provides the waveform theoretical basis for the use of a flattened Gaussian beam in a laser altimeter.

ON GENERALIZED SPHERICAL SURFACES IN EUCLIDEAN SPACES

  • Bayram, Bengu;Arslan, Kadri;Bulca, Betul
    • Honam Mathematical Journal
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    • v.39 no.3
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    • pp.363-377
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    • 2017
  • In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1)-space ${\mathbb{E}}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$ respectively. We have shown that the generalized spherical surfaces of first kind in ${\mathbb{E}}^4$ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in ${\mathbb{E}}^4$. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.