• Title, Summary, Keyword: Fourier Sine Transform

### AN APPROXIMATION OF THE FOURIER SINE TRANSFORM VIA GRÜSS TYPE INEQUALITIES AND APPLICATIONS FOR ELECTRICAL CIRCUITS

• DRAGOMIR, S.S.;KALAM, A.
• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.33-45
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• 2002
• An approximation of the Fourier Sine Transform via Gr$\ddot{u}$ss, Chebychev and Lupaş integral inequalities and application for an electrical curcuit containing an inductance L, a condenser of capacity C and a source of electromotive force $E_0P$(t), where P (t) is an $L_2$-integrable function, are given.

### FOURIER'S TRANSFORM OF FRACTIONAL ORDER VIA MITTAG-LEFFLER FUNCTION AND MODIFIED RIEMANN-LIOUVILLE DERIVATIVE

• Jumarie, Guy
• Journal of applied mathematics & informatics
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• v.26 no.5_6
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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.

### A Study on Wavelet Application for Signal Analysis (신호 해석을 위한 웨이브렛 응용에 관한 연구)

• Bae, Sang-Bum;Ryu, Ji-Goo;Kim, Nam-Ho
• Proceedings of the Korea Institute of Convergence Signal Processing
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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.

### Measurement of Mode Shape By Using A Scanning Laser Doppler Vibrometer (스캐닝 레이저 도플러 진동 측정기를 이용한 모드 측정)

• Kang, Min-Sig
• Proceedings of the KSME Conference
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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.

### Measurement of Mode Shape By Using A Scanning Laser Doppler Vibrometer (스캐닝 레이저 도플러 진동계를 이용한 모드 해석)

• Gang, Min-Sik
• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.10
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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.

### A NEW APPLICATION OF ADOMIAN DECOMPOSITION METHOD FOR THE SOLUTION OF FRACTIONAL FOKKER-PLANCK EQUATION WITH INSULATED ENDS

• Ray, Santanu Saha
• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1157-1169
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• 2010
• This paper presents the analytical solution of the fractional Fokker-Planck equation by Adomian decomposition method. By using initial conditions, the explicit solution of the equation has been presented in the closed form and then the numerical solution has been represented graphically. Two different approaches have been presented in order to show the application of the present technique. The present method performs extremely well in terms of efficiency and simplicity.

### A Study on Frequency-Time Plane Analysis of Wavelet (웨이브렛의 주파수-시간 평면 해석에 관한 연구)

• Bae, Sang-Bum;Ryu, Ji-Goo;Kim, Nam-Ho
• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.2
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• pp.451-454
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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 depends 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.

### EXACT SOLUTIONS OF GENERALIZED STOKES' PROBLEMS FOR AN INCOMPRESSIBLE COUPLE STRESS FLUID FLOWS

• SIDDIQUE, IMRAN;UMBREEN, YOUSRA
• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.507-519
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• 2019
• The ground for this paper is to examine the generalized Stokes' first and second issues for an incompressible couple pressure liquid under isothermal conditions. Exact solutions for each problem are acquired by using the Laplace transform (LT) with respect to the time variable t and the sine Fourier transform (FT) with respect to the y-variable. Further, a comparison is given of the obtained results and the results of Devakar and Lyengar  and by using the four inverse Laplace transform algorithms (Stehfest's, Tzou's, Talbot, Fourier series) in the space time domain utilizing a numerical methodology. Moreover, velocity profiles are plotted and considered for various occasions and distinctive estimations of couple stress parameters. At the end, the outcomes are exhibited by graphs and in tabular forms.

### APPARENT INTEGRALS MOUNTED WITH THE BESSEL-STRUVE KERNEL FUNCTION

• Khan, N.U.;Khan, S.W.
• Honam Mathematical Journal
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• v.41 no.1
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• pp.163-174
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• 2019
• The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.