• Current Optics and Photonics
• /
• v.2 no.4
• /
• pp.315-323
• /
• 2018

A new multiple-image encryption scheme that is based on a compressive ghost imaging concept along with a Fourier transform sampling principle has been proposed. This further improves the security of the scheme. The scheme adopts a Fourier transform to sample the original multiple-image information respectively, utilizing the centrosymmetric conjugation property of the spatial spectrum of the images to obtain each Fourier coefficient in the most abundant spatial frequency band. Based on this sampling principle, the multiple images to be encrypted are grouped into a combined image, and then the compressive ghost imaging algorithm is used to improve the security, which reduces the amount of information transmission and improves the information transmission rate. Due to the presence of the compressive sensing algorithm, the scheme improves the accuracy of image reconstruction.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.4
• /
• pp.785-803
• /
• 2004

We research properties of analytic functions which are exponentially decreasing or increasing. Also we show that the space of test functions is dense in the space of extended Fourier hyper-functions, and that the Fourier transform of the space of extended Fourier hyperfunctions into itself is an isomorphism and Parseval's inequality holds.

• The Journal of the Acoustical Society of Korea
• /
• v.35 no.1
• /
• pp.8-15
• /
• 2016

As a generalized form of the conventional Fourier transform, fractional Fourier transform (FrFT) can analyze a signal at intermediate domain between time and frequency domains with a transform order ${\alpha}$. Especially, FrFT has a number of advantages in the analysis of LFM (Linear Frequency Modulation) signals due to its robustness to noise. In this paper, we have proposed a new method to detect and estimate the distance of the target from the FrFT spectrum of the received echo signal. Experimental results have validated the proposed method, and shown that reliable target distance could be estimated in noise and reverberation environments.

• Journal of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.991-1017
• /
• 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.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
• /
• 2001.10a
• /
• pp.169-173
• /
• 2001

This study presents the results of decoupling of free decay roll test data by discrete wavelet transform. Free roll decay test was performed to decide the coefficients of damping terms in equation of motion. During the experiment, a slight yaw motion was found while the model was in the free roll decay motion. Discrete wavelet transform was applied to the signal to extract the pure roll motion. The results were compared to those of the Fourier transform. DWT was able to decouple the two signals efficiently while the Fourier transform was not.

• Proceedings of the Korean Society of Rheology Conference
• /
• 2000.05a
• /
• pp.62-65
• /
• 2000

• Proceedings of the Optical Society of Korea Conference
• /
• 2001.08a
• /
• pp.80-81
• /
• 2001

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
• /
• v.21 no.3
• /
• pp.75-81
• /
• 2007

Recently the subject of "wavelet analysis" has be drawn by both mathematical and engineering application fields such as Signal Processing, Compression/Decomposition, Wavelet-Neural Network, Statistics and etc. Even though its similar to Fourier analysis, wavelet is a versatile tool with much mathematical content and great potential for applications. Especially, wavelet transform uses localizable various mother wavelet functions in time-frequency domain. Therefore, wavelet transform has good time-analysis ability for high frequency component, and has good frequency-analysis ability for low frequency component. Using the discriminative ability is more easy method than other conventional techniques. In this paper, Morlet wavelet transform was applied to discriminate the kind of line fault by acquired data from real power transformation network. The experimental result presented that Morlet wavelet transform is easier, and more useful method than the Fast Fourier Transform(FFT).

• Proceedings of the KSR Conference
• /
• 2008.06a
• /
• pp.841-848
• /
• 2008

This paper examined dynamic characteristics of high speed trains using a time varying frequency transform. Fourier transform based methods are frequently used for the calculation of the dynamic characteristics of trains in the frequency domain, but they cannot represent the time-varying characteristics. Therefore it is necessary to examine their characteristics using a time-varying frequency transform. For the examination, the non-stationary vibration of wheelset, bogie, and carbody are measured using accelerometers and stored in a data aquisition system. They are processed with localization of the data by modulating with a window function, and Fourier transform is taken to each localized data, called the short-time Fourier transform. From the processed results, time varying auto-spectral density, cross-spectral density, frequency response, and coherence functions have been calculated. From the analysis, it is confirmed that the time varying frequency transform is a useful method for analyzing the dynamic characteristics of high speed trains.

• Journal of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.265-294
• /
• 2004

In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier-Feynman transforms. Also, we evaluate the conditional Fourier-Feynman transforms of the functions of the forms exp {$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}$\Phi$($\chi$(T)), exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}$\Phi$($\chi$(T)) which are of interest in Feynman integration theories and quantum mechanics.