• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1101-1121
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• 2008

One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.

• 융합신호처리학회 학술대회논문집
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• 한국신호처리시스템학회 2005년도 추계학술대회 논문집
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• pp.302-305
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• 2005

Recently, many methods to analyze signal have been proposed and representative methods are the Fourier transform and wavelet transform. In these methods, the Fourier transform represents signal with combination cosine and sine at all locations in the frequency domain. However, it doesn't provide time information that particular frequency occurs in signal and denpends on only the global feature of the signal. So, to improve these points the wavelet transform which is capable of multiresolution analysis has been applied to many fields such as speech processing, image processing and computer vision. And the wavelet transform, which uses changing window according to scale parameter, presents time-frequency localization. In this paper, we proposed a new approach using a wavelet of cosine and sine type and analyzed features of signal in a limited point of frequency-time plane.

• Structural Engineering and Mechanics
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• 제24권1호
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• pp.63-89
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• 2006

Geometric imperfections have an important influence on the buckling response of structural components. This paper describes an experimental technique for determining imperfections in long (5.7 m) structural members using a series of overlapping measurements. Measurements were performed on 31 austenitic stainless steel sections formed from three different production routes: hot-rolling, cold-rolling and press-braking. Spectral analysis was carried out on the imperfections to obtain information on the periodic nature of the profiles. Two series were used to model the profile firstly the orthogonal cosine and sine functions in a classic Fourier transform and secondly a half sine series. Results were compared to the relevant tolerance standards. Simple predictive tools for both local and global imperfections have been developed to enable representative geometric imperfections to be incorporated into numerical models and design methods.

• Journal of Advanced Marine Engineering and Technology
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• 제14권4호
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• pp.46-56
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• 1990

Stress analysis of axi-symetric body with non-symetric loading and non-symetric given displacements is investigated in this paper using the finite element method. As the non-symetric load and non-symetric given displacements of axi-symetric body are generally periodic functions of angle .theta., the nodal forces and nodal displacements can be expanded in cosine and sine series, that is, Fourier series. Furthermore, using Euler's formula, the cosine and sine series can be converted into exponential series and it is prooved that the related calculus become more clear. Substituting the nodal displacements expanded in Fourier series into the strain components of cylindrical coordinates system, the element strains are expressed in series form and by the principal of virtual work, the element stiffness martix and element load vector are obtained for each order. It is also showed that if the non-symetric loads are even or odd functions of angle ${\theta}$ the stiffness matrix and load vector of the system are composed with only real numbers and relatively small capacity fo computer memory is enough for calculation.

• 한국전기전자재료학회논문지
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• 제13권1호
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• pp.39-46
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• 2000

An analysis of the free vibration for the metal-piezoceramic laminated thin plates is described. The purpose of this study is to develop a equivalent method for the free vibration analysis of metal-piezoce-ramic laminated thin plate which are not sysmmetric about the adhered layer and the piezoelectric effect. In order to confirm the validity of the vibration analysis, double Fourier sine series is used as a modal displacement function of a metal-piezoceramic laminated thin plate and applied to the free vibration analysis of the plate under various boundary conditions.

• Advances in nano research
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• 제16권2호
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• pp.175-186
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• 2024

Dynamical behaviors of one-dimensional (1D) nano-sized structures are of great importance in nanotechnology applications. Therefore, the torsional dynamic response of functionally graded nanorods which could be used to model the nano electromechanical systems or micro electromechanical systems with torsional motion about the center of twist is examined based on the theory of strain gradient nonlocal elasticity in this work. The mathematical background is constructed based on both strain gradient theory and Eringen's nonlocal elasticity theory. The equation of motions and boundary conditions of radially functionally graded nanorods are derived using Hamilton's principle and then transformed into the eigenvalue analysis by using Fourier sine series. A general coefficient matrix is obtained to assemble the Stokes' transformation. The case of a restrained functionally graded nanorod embedded in two elastic springs against torsional rotation is then deeply investigated. The effect of changing the functionally graded index, the stiffness of elastic boundary conditions, the length scale parameter and nonlocal parameter are investigated in detail.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2005년도 추계종합학술대회
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• pp.451-454
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• 2005

현재, 신호를 해석하기 위한 많은 방법들이 제시되고 있으며, 대표적인 방법으로는 퓨리에 변환과 웨이브렛 변환이 있다. 이러한 방법들에서, 퓨리에 변환은 모든 주파수 범위에 대해 cosine과 sine 파형의 조합으로써 신호를 표현하지만, 신호 내에서 특정 주파수 성분이 발생한 시간정보를 제공하지 않으며, 분석 신호의 전체적인 특징만을 나타낸다. 따라서 이러한 한계를 극복하기 위해, 다중해상도 해석이 가능한 웨이브렛 변환이 음성과 영상처리, 컴퓨터 비전 등의 광범위한 분야에서 응용되고 있다. 그리고 웨이브렛 변환은 스케일 변수에 따라 변화하는 윈도우를 사용하여 시간-주파수 국부성을 나타낸다. 본 논문에서는 cosine과 sine 형태의 웨이브렛을 사용하여, 퓨리에 변환의 새로운 접근법을 제시하였으며, 주파수-시간 평면의 유한한 지점에서 신호의 특징을 분석하였다.

• 대한기계학회논문집A
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• 제24권10호
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• pp.2560-2567
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• 2000

When spatially dense velocity distribution is measured by a scanning laser Doppler vibrometer, the Fourier transform method provides the real and imaginary parts of the mode shapes in the form of a polynomial. However the Fourier transform method is often impractical because the independent decomposition property of cosine and sine components into real and imaginary parts, respectively, does not hold due to the leakage problem which commonly occurs in the Fourier transform of harmonic signals. To deal with this problem, a Hilbert transform method is newly proposed in this article. The proposed method is free from the leakage problem and relatively robust to the scanning error. A simulation example is provided to verify the effectiveness of this method.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집A
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• pp.420-425
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• 2000

When spatially dense velocity distribution is measured by a scanning laser Doppler vibrometer, the Fourier transform method provides the real and imaginary parts of the mode shapes in the form of a polynomial. However the Fourier transform method is often impractical because the independent decomposition property of cosine and sine components into real and imaginary parts, respectively, does not hold due to the leakage problem which commonly occurs in the Fourier transform of harmonic signals. To deal with this problem, a Hilbert transform method is newly proposed in this article. The proposed method is free from the leakage problem and relatively robust to tire scanning error. A simulation example is provided to verify the effectiveness of this method.

• 한국정보통신학회논문지
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• 제15권8호
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• pp.1756-1763
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• 2011

본 연구에서는 생물학적 모방에 따른 물고기 로봇의 직진유영에 관한 연구로써, Liu 등이 제안한 꼬리 모션 함수를 푸우리에 급수 전개의 7차 항까지 고려한 제안된 방법과 일반적인 사인함수만으로 근사한 방법과 비교하여 모의실험 하였다. 일반적으로 로봇 물고기의 꼬리 링크의 길이가 길어지고 링크가 많을 경우, 로봇 물고기의 꼬리 모션 함수의 말단 회전 관절 궤적은 사인 함수의 모양과 매우 다르다. 그러므로 로봇 물고기의 꼬리 궤적을 단순한 푸우리에 급수 전개의 기본파 성분만으로 근사하기에는 문제가 있다. 제안된 방법과 일반적인 사인함수만으로 근사한 방법의 모의실험 결과 제안된 방법이 로봇 물고기의 추력과 속도에서 10%정도 뛰어남을 보였다.