• Title/Summary/Keyword: Fourier transform

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Convergence Properties of an Iterative Algorithm for Phase Retrieval (위상복원을 위한 iterative 알고리즘의 수렴 특성)

  • Kim, Woo-Shik
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.46 no.3
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    • pp.60-67
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    • 2009
  • The phase retrieval problem is a problem of reconstructing a signal or the phase of Fourier transform of the signal from the magnitude of its Fourier transform. In this paper we address the problem of reconstructing an unknown signal from the magnitude of its Fourier transform and the magnitude of Fourier transform of another signal that is given by the addition of the desired signal. After we briefly mention the uniqueness conditions under which a signal can be uniquely specified from the given information and key equations of the iterative algorithm, we present mathematical background that the iterative algorithm converges to the desired signal, present an example that illustrates the performance of the reconstruction algorithm, and show its convergence property.

Design of phase-only diffractive pattern elements using a two-stage iterative Fourier transform algorithm (2단계 iterative Fourier transform 알고리즘을 이용한 위상형 회절무늬소자 설계)

  • 정필호;조두진
    • Korean Journal of Optics and Photonics
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    • v.11 no.1
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    • pp.47-57
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    • 2000
  • A two-stage iterative Fourier transform algorithm, based on hybrid input-output algorithm and new Pnoise algorithm, is used to design continuous and quantized phase-only diffractive pattern elements which produce arbitrary given intensity patterns via Fraunhofer diffraction. Numerical results for two $128\times128$ binary patterns and two grayscale patterns are compared with those of other algorithms. It is found that the algorithm yields better signal-to-noise ratio and even better uniformity with slightly lower diffraction efficiency than other algorithms. We investigated the dependence of performance on parameters used in the algorithm, size of noise region, and the number of phase levels for quantized elements. In the case of quantized phase elements, the size of noise region plays a greater role in determining the performance of the algorithm than given intensity pattern itself. tself.

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Application of Phase-shifting Method using fourier Transform to Measurement of In-plane Displacement by Speckle Interferometry

  • Kim, Myung-Soo;Baek, Tae-Hyun;Morimoto, Yoshiharu;Fujigaki, Motoharu
    • Journal of the Korean Society for Nondestructive Testing
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    • v.25 no.3
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    • pp.171-177
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    • 2005
  • Phase-shifting method using Fourier transform (PSM/FT) has been applied to measurement of in-plane displacement of a specimen. Thirty-two interference fringe patterns each of which has different phase of ${\pi}/16$ radian have been gathered from a specimen with in-plane displacement. Low-pass filtering by 2-D Fourier transform is used to suppress spatial noise of the fringe patterns. ${\alpha}-directional$ Fourier transform for PSM/FT is performed by use of the low-pass filtered 32 fringe patterns. Two kinds of specimens are used for experiment. One is a rectangular steel plate and the other one is a rectangular steel plate containing a circular hole at the center. In-plane displacement of each specimen is measured by PSM/FT, and calculated by finite element method (ANSYS) for comparison. The results are quite comparable, so that PSM/FT can be applied to measurement of in-plane displacement.

Estimation of target distance based on fractional Fourier transform analysis of active sonar linear frequency modulation signals (능동소나 linear frequency modulation 신호의 fractional Fourier transform 분석에 기반한 표적의 거리 추정)

  • Hyung, Sungwoong;Park, Myungho;Hwang, Soobok;Bae, Keunsung
    • The Journal of the Acoustical Society of Korea
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    • v.35 no.1
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    • pp.8-15
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    • 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.

BOEHMIANS ON THE TORUS

  • Nemzer, Dennis
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.831-839
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    • 2006
  • By relaxing the requirements for a sequence of functions to be a delta sequence, a space of Boehmians on the torus ${\beta}(T^d)$ is constructed and studied. The space ${\beta}(T^d)$ contains the space of distributions as well as the space of hyperfunctions on the torus. The Fourier transform is a continuous mapping from ${\beta}(T^d)$ onto a subspace of Schwartz distributions. The range of the Fourier transform is characterized. A necessary and sufficient condition for a sequence of Boehmians to converge is that the corresponding sequence of Fourier transforms converges in $D'({\mathbb{R}}^d)$.

A Shape feature extracting of WBC using UNL Fourier transform (UNL Fourier Transform을 이용한 백혈구 모양 특징 추출)

  • 이성환;김지윤;유채곤;황치정
    • Proceedings of the Korean Information Science Society Conference
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    • pp.505-507
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    • 2000
  • 현재 백혈병 진단에서 사용중인 방법은 골수영상을 획득하고 이를 관찰하여 비정상의 백혈구의 형태, 백혈구 핵의 크기와 추출된 골수에서의 백혈구가 차지하는 비율을 이용하여 진단하고 있다. 비정상적인 모양을 띠고 있는 백혈구의 검출은 백혈병 진단에 있어 중요한 정보로 사용된다. 백혈구의 이상 형태중 다수의 구멍이 있는 백혈구는 검출하기 위해 골수영상에서 백혈구 영역을 추출하고 이에 대해 UNL transform을 이용하여 모양 특징을추출하였다. UNL Fourier transform은 원영상의 이동(translation), 회전(rotation), 확대/축소(scale)에 대해 불변인 성질을 지니므로 이를 이용해 백혈구의 모양 특징을 추출하고 유사도 검색을 통해 비정상의 백혈구를 검출하였다.

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Research on Multiple-image Encryption Scheme Based on Fourier Transform and Ghost Imaging Algorithm

  • Zhang, Leihong;Yuan, Xiao;Zhang, Dawei;Chen, Jian
    • Current Optics and Photonics
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    • v.2 no.4
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    • pp.315-323
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    • 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.

Feature Extraction of Fault Current using Fourier Transform in the Multi-Shot Reclosing Scheme (푸리에 변환을 이용한 다중 재폐로방식에서의 사고전류 특징 추출)

  • O, Jeong-Hwan;Yun, Sang-Yun;Kim, Jae-Cheol
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.49 no.2
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    • pp.50-55
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    • 2000
  • This paper presents the feature extraction of fault currents related to the multi-shot reclosing scheme in the power distribution system. In order to get the fault current waveform, we have measured the fault currents by the fault recorders which have been installed at the secondary side of 154/22.9[kV] substation transformer. These waveforms are classified into temporary and permanent fault. For the classified waveforms, Fourier transform is used to extract the feature of the fault current waveforms. After the waveforms are analyzed by using Fourier transform, the magnitude spectrum and the relative variation of THD (Total Harmonic Distortion) are calculated. And then the relative variation of THD is great in the temporary faults, and is small in the permanent faults.

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