• 소음진동
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• 제7권5호
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• pp.747-756
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• 1997

Wigner-Ville distribution which is a time-frequency analysis has a fatal drawback, when the signal has multiple components. This is the cross-talk and often causes a neagative value in the distribution. Wingner-Ville distriution is an expression of power, therefore the cross-talk must be avoided. Smoothing the Wigner-Ville distribution by convoluting it with a window, is most commonly used to reduce the cross-talk. There can be infinite number of distributions depending on the windows. But, the smoothing reduces resolution in time-frequency plane; this motives to design a more effective window in reducing cross-talk while remaining resolution. The domain in which the cross-talk and legitimate components can be easily distinguished, is the ambiguity function. In the ambiguity function domain, the legitimate components appear as linear lines passing through the orgine. But, the cross-talk is widely distributes in the ambiguity function plane. Based on the relative distributions of cross-talk and legitimate components, rotating window can be designed to minimize cross-talk. Applying the rotating window to the ambiguity function corresponds to smoothing the Wigner-Ville distribution. Therefore, the effects of rotating window is estimated in terms of the bias error due to smooting the Wigner-Ville distribution. By applying the rotating window, not only the Wigner-Ville distribution but also its properties are changed. The properties of the new distribution are checked, in order to complete analyzing the rotating window.

• 소음진동
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• 제7권2호
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• pp.319-329
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• 1997

Wigner-Ville distribution has been recognized as a useful tool and applied to various types of mechanical noise and vibration signals, but its limitation which mainly comes from the cross-talk has not been well addressed. The cross-talk takes place for a signal with multiple components, simply because the Wigner-Ville distribution is a bilinear transform. The cross-talk often causes a negative value in the distribution. This cannot be accepted for the Wigner- Ville distribution, because it is an expression of power. Smoothing the Wigner-Ville distribution by convoluting it wih a window, is most commonly used to reduce the cross-talk. There can be infinite number of distributions depending on the windows. In this paper, we attempted to develop a distribution which is the best or the optimal in reducing the cross-talk. This could be possible by employing the ambiguity function. For a general signal, however it is difficult to express the ambiguity function as a mathematically closed form. This requires an appropriate modeling to make such expression possible. We approximated the Wigner-Ville distribution as a sum of linear segments. In the ambiguity function domain, the legitimate components are reflected as linear lines passing through the origin. Every lines has its own length and slope. But, the cross-talk is widely distributed in the ambiguity function plane. Based on this realization, we proposed a two-dimensional window which is in fact 'rotating window', that can eliminate cross-talk component. The rotating window is examined numerically and is found to have a better performance in reducing the cross-talk than conventional windows, the Gaussian window.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.827-832
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• 2003

There has been a number methods for the presentation of time-frequency analysis of non-stationary signal. In this paper, STFT(short time Fourier transform), wavelet transform, Wigner distribution, and higher order Wigner distribution are discussed in details with simulation signals. They are also applied to the analysis of the wave propagation of a semi finite beam. Wigner distribution and higher order Wigner distribution have good time-frewuency resolutions. Wavelet transform is required for impact analysis but should be applied carefully. STFT suffers from time-frequency resolutions. Each method is has its advantage and disadvantage depending on each application signals.

• 소음진동
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• 제6권3호
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• pp.341-347
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• 1996

진동해석을 이용한 기계계통의 진단에는 시간영역(time domain)에서의 해석 과 FFT(Fast Fourier Transform)를 이용한 주파수영역(frequency domain)에서의 해석 을 생각할 수 있다. 이중 FFT 방법은 고속연산기의 출현과 물리적인 이해의 편이성 등오로 인하여 널리 사용되고 있으나, 시간 함수인 비정상 상태신호(nonstationary signal)의 경우는 주파수영역 해석만으로는 물리적 이해를 구하는데는 한계가 있다. 그래서, 최근 신호처리기법 분야에서는 주파수영역 해석과 시간영역 해석을 보완적 으로 표현할 수 있는 기간-주파수영역 해석기법에 많은 연구가 진행되고 있다. 그중 대표적인 신호처리 기법은 Wigner-Ville Distribution이며, 특히 본 Wigner-Ville Distribution은 많은 물리적 의미를 갖고 있어 주요 연구 대상이며, 많은 응용분야 를 갖고 있다. 그러나, 기계계통중 회전체의 진동신호을 분석하여 고장 진단 및 감시를 용이하기 위해서는 새로운 형태의 시간.주파수영역 해석기법이 필요하다. 본 논문에서는 회전체의 진동신호 분석이 용이하도록 물리적인 의미와 응용상에 중점을 둔 방향서 Wigner-Ville 분포라는 시간-주파수 분석기법을 제안하였고, 회전체를 이용한 실험을 실시하였다. 그 결과 제안된 방향성 Wigner-Ville Distribution은 회전체 진동신호를 시간-주파수 영역에서 잘 표현하고 있으며, 특히 회전체의 수직 및 수평방향 진동신호로 부터 얻어지는 방향성 Wigner-Ville Distribution은 각 주파수 성분의 방향성 정보를 갖고 있어 이를 회전체의 고장 진단 및 감시에 이용 하였다.

• 한국광학회:학술대회논문집
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• 한국광학회 2009년도 동계학술발표회 논문집
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• pp.449-450
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• 2009

위그너 분포 함수 측정을 통하여 진행하는 laser beam의 상관함수와 진행 특성들을 연구하였다. 위그너 분포 함수는 진행하는 laser beam의 total degree of coherence, beam quality parameter, 그리고 근접장 및 원거리장의 정보들을 보여준다. 위그너 분포 함수를 이용하여 공간상관 함수와 방향상관 함수를 구할 수 있으며, 이를 Schmidt mode decomposition을 이용하여 분석하면 laser beam의 보다 여러가지 특성들을 분석 할 수 있다. 이렇게 분석된 eigenmode들은 진행하는 laser beam의 보다 정확한 coherence 특성을 이해하게 해준다.

• 로봇학회논문지
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• 제5권1호
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• pp.32-40
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• 2010

This paper proposes the technique of estimating the pipe thickness using the measured group velocity. To measure the group velocity from the accelerometer data in the frequency domain, Wigner-Ville distribution is utilized, which interprets the waveform of the shock wave. Using this measured group velocity, this paper proposes the technique to estimate the thickness of pipes with the impact on the pipe. The group velocity is estimated by the modeling correlation between the group velocity and the thickness of the pipe based on the propagation velocities. The correlation model between thickness and group velocity has been proved through the real experiments. The measured group velocity in the frequency-domain is the maximum at the center frequency of the bending waves in the modeling of the group velocity. In addition to these, a smoothing technique for analyzing lamb wave Wigner-Ville distribution has been introduced to improve the reliability of the data acquisition.

• ETRI Journal
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• 제41권1호
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• pp.42-51
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• 2019

The rainbow hologram provides views of reconstruction with rainbow color within a large viewing zone. In our recent paper, a Fourier rainbow holographic display using diffraction grating and a white-light LED source was introduced. In this technique, the rainbow effect is realized by the dispersion of white-light source on diffraction grating, while the slit is implemented numerically by reducing the demands of the space-bandwidth product of the display. This paper presents a novel analysis on the visual perception of the Fourier rainbow holographic display using Wigner distribution. The view-dependent appearance of the image, including multispectral field of view and viewing zone, is investigated considering the observer and the display parameters. The resolution of the holographic view is also investigated. For this, a new quantitative assessment for image blur is introduced using Wigner distribution analysis. The analysis is supported with numerical simulations and experimentally captured optical reconstructions for the holograms of the computer model and real object generated with different slit size, reconstruction distance, and different observation conditions.

• 한국광학회지
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• 제11권6호
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• pp.385-389
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• 2000

본 논문에서는 원형 대칭 광 시스템에 대한 초점 심도를 증가시키기 위해 Wigner 분포 함수(WDF)로 유도된 위상 지연 함수를 이용한다. 1차원 신호에 대한 WDF는 위상-공간($\chi,\zeta$)상의 2차원 함수로 표현되고 Strehl 비 (SR)를 이용해 정규화된 복사조도로 나타낸다. 초점 심도의 증가는 WDF 공간상에서 간단한 조작으로 자유공간 전파의 특성을 나타내는 전단 기울기 $\alpha$을 부여함으로서 달성된다. 또한 $\alpha$을 초점 심도의 항 $\delta_z$로 표현함으로서 위상 지연 함수를 통해 정량적으로 초점특성을 평가할 수 있는 방법을 제안한다. 제안된 방법으로 수치 해석한 결과를 다른 접근법으로 수행되었던 연구결과와 비교한다.

• 한국광학회지
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• 제11권6호
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• pp.441-446
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• 2000

Balanced Homodyne Detection 방법으로 국소 진동자의 위상을 조절해 주면서, 각 위상에 대하여 광전류를 측정하여 전류세기의 분포함수를 구하여 이 값을 라돈 역변환을 포함한 Filtered Back Projection하여 빛의 양자역학적 상태를 규정하는 위그너 함수를 구하고 이로부터 간접적으로 밀도행렬을 구한다. 또 위상에 관계없이 구해진 분포함수에서 Pattern함수를 이용하여 밀도행렬을 구할 수 있다. 본 연구에서는 위의 모든 과정을 전산시늉을 통하여 여러 양자역학적 상태 입력 광에 대하여 예측되는 위그너 함수와 밀도 행렬을 구하였다.

• 한국전기전자재료학회논문지
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• 제23권2호
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• pp.103-117
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• 2010

In this study, the heart rate variability(HRV) signal of operating patient was acquired according to anesthesia progress and identified to evaluation possibility of depth of anesthesia in each anesthesia stage. The HRV signal was analyzed time-frequency domain applied to Wigner-Ville distribution method, the characteristic parameters were extracted for evaluation of depth of anesthesia in each anesthesia stage. The progress of general anesthesia was divided into the states of pre-operation, induction of anesthesia, operation, awaking and post-operation.