• 한국정보통신학회논문지
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• 제17권3호
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• pp.540-545
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• 2013

Fractional 푸리에변환(Fractional Fourier Transform : FRFT)은 기존의 푸리에 변환의 일반화된 형태로서, 양자역학분야에서 처음 소개되었다. FRFT가 가지는 시간-주파수 영역에서의 단순하면서도 유용한 특성으로 인하여, 지금까지 소나 및 레이더 신호처리 분야에서 많은 연구결과들이 발표되었으며, 푸리에 변환을 활용한 기존의 방법보다 우수한 연구결과를 보여 왔다. 본 논문에서는 LFM(Linear Frequency Modulation)신호들이 겹쳐져 수신되었을 경우에 이들 신호들을 검출하고 분리하기 위해 FRFT를 이용하였다. 실험결과 수신된 LFM 신호들을 FRFT 영역에서 효율적으로 검출하고 분리가 가능함을 확인하였다.

• 호남수학학술지
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• 제38권3호
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• pp.613-623
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• 2016

As a generalization of the Fourier transform, the fractional Fourier transform plays an important role both in theory and in applications of signal processing. We present a new approach to reach a uniform sampling theorem in the shift-invariant spaces associated with the fractional Fourier transform domain.

• 전자공학회논문지B
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• 제31B권5호
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• pp.26-33
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• 1994

Phase retrieval is concerned with the reconstruction of a signal from its Fourier transform magnitude (or intensity), which arises in many areas such as X-ray crystallography, optics, astronomy, or digital signal processing. In such areas, the Fourier transform phase of the desired signal is lost while measuring Fourier transform magnitude (F.T.M.). However, if a reference 'signal is added to the desired signal, then, in the Fourier trans form magnitude of the added signal, the Fourier transform phase of the desired signal is encoded. This paper addresses uniqueness and retrieval of the encoded Fourier phase of a multidimensional signal from the Fourier transform magnitude of the added signal along with the Fourier transform magnitude of the desired signal and the information of the additive reference signal. In Part I, several conditions under which the desired signal can be uniquely specified from the two Fourier transform magnitudes and the additive reference signal are presented. In Part II, the development of non-iterative algorithms and an iterative algorithm that may be used to reconstruct the desired signal(s) is considered.

• 전자공학회논문지B
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• 제31B권5호
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• pp.34-41
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• 1994

Phase retrieval is concerned with the reconstruction of a signal from its Fourier transform magnitude (or intensity), which arises in many areas such as X-ray crystallography, optics, astronomy, or digital signal processing In such areas, the Fourier transform phase of the desired signal is lost while measuring Fourier transform magnitude (F.T.M.). However, if a reference 'signal is added to the desired signal, then, in the Fourier trans form magnitude of the added signal, the Fourier transform phase of the desired signal is encoded This paper addresses uniqueness and retrieval of the encoded Fourier phase of a multidimensional signal from the Fourier transform magnitude of the added signal along with Fourier transform magnitude of the desired signal and the information of the additive reference signal In Part I, several conditions under which the desired signal can be uniquely specified from the two Fourier transform magnitudes and the additive reference signal are presented In Part II, the development of non-iterative algorithms and an iterative algorithm that may be used to reconstruct the desired signal (s) is considered

• Korean Journal of Mathematics
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• 제12권2호
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• pp.193-200
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• 2004

We shall introduce the notion of the windowed Fourier transform in $\mathbb{Q}_p$ and show that, for any given function $g{\in}L^2(\mathbb{Q}_p)$ of norm, the windowed Fourier transform of $f$ with respect to $g$ be a function of norms, and moreover be expressible to a summation form. The results obtained in this paper will be usable to the field of research in data compression for signal processing according to the following scheme.

• 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.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2003년도 봄 학술발표회 논문집
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• pp.249-256
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• 2003

To investigate the safety and stability of the concrete lining, numerous studies have been conducted over the years and several methods have been developed. Most signal processing method of NDT techniques has based on the Fourier analysis. However, the application of Fourier analysis to analyze recorded signal shows results only in frequency domain, it is not enough to analyze transient waves precisely. In this study, a new NDT technique .using the wavelet theory was employed for the analysis of non-stationary wave propagation induced by mechanical impact in the concrete lining. The wavelet transform of transient signals provides a method for mapping the frequency spectrum as a function of time. To verify the availability of wavelet transform as a time- frequency analysis tool, model experiments have been conducted on the concrete lining model. From this study, it was found that the contour map by Wavelet transform provides more distinct results than the power spectrum by Fourier transform and it was concluded that Wavelet transform was an effective tool for the experimental analysis of dispersive waves in concrete structures.

• 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.

• Smart Structures and Systems
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• 제1권2호
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• pp.185-215
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• 2005

Advanced signal processing techniques have been long introduced and widely used in structural health monitoring (SHM) and nondestructive evaluation (NDE). In our research, we applied several signal processing approaches for our embedded ultrasonic structural radar (EUSR) system to obtain improved damage detection results. The EUSR algorithm was developed to detect defects within a large area of a thin-plate specimen using a piezoelectric wafer active sensor (PWAS) array. In the EUSR, the discrete wavelet transform (DWT) was first applied for signal de-noising. Secondly, after constructing the EUSR data, the short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were used for the time-frequency analysis. Then the results were compared thereafter. We eventually chose continuous wavelet transform to filter out from the original signal the component with the excitation signal's frequency. Third, cross correlation method and Hilbert transform were applied to A-scan signals to extract the time of flight (TOF) of the wave packets from the crack. Finally, the Hilbert transform was again applied to the EUSR data to extract the envelopes for final inspection result visualization. The EUSR system was implemented in LabVIEW. Several laboratory experiments have been conducted and have verified that, with the advanced signal processing approaches, the EUSR has enhanced damage detection ability.

• Journal of Information Processing Systems
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• 제12권4호
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• pp.555-576
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• 2016

In the conventional clustering algorithms, an object could be assigned to only one group. However, this is sometimes not the case in reality, there are cases where the data do not belong to one group. As against, the fuzzy clustering takes into consideration the degree of fuzzy membership of each pixel relative to different classes. In order to overcome some shortcoming with traditional clustering methods, such as slow convergence and their sensitivity to initialization values, we have used the Harmony Search algorithm. It is based on the population metaheuristic algorithm, imitating the musical improvisation process. The major thrust of this algorithm lies in its ability to integrate the key components of population-based methods and local search-based methods in a simple optimization model. We propose in this paper a new unsupervised clustering method called the Fuzzy Harmony Search-Fourier Transform (FHS-FT). It is based on hybridization fuzzy clustering and the harmony search algorithm to increase its exploitation process and to further improve the generated solution, while the Fourier transform to increase the size of the image's data. The results show that the proposed method is able to provide viable solutions as compared to previous work.