• 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.

• 한국음향학회지
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• 제26권3호
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• pp.123-128
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• 2007

본 논문에서는 수중 천이 신호에 대한 식별 알고리즘을 제안한다. 일반적으로 해양의 배경잡음은 스펙트럼 특성 및 에너지 변화가 적은 정재성을 갖는 반면에 천이 신호는 스펙트럼 및 에너지 변화가 큰 비정재성을 가진다. 따라서 수중 천이 신호 식별을 위하여 선행되어져야 하는 수중 천이 신호 탐지에서는 프레임 단위로 스펙트럼 변이와 에너지 변화를 이용한다. 제안한 수중 천이 신호 식별 알고리즘에서는 특징 벡터를 추출하기 위하여 위그너-빌 분포 함수를 기반으로 고유치 분해를 이용한다. 추출된 특징 벡터를 기반으로 탐지된 수중 천이 신호의 특징 벡터와 식별하고자 하는 데이터베이스에 있는 기준 신호의 특징 벡터와의 상관 값을 프레임 단위로 계산하고, 각 클래스별로 프레임 사상도를 산출하여 최대 값을 갖는 기준 신호로 탐지된 수중 천이 신호를 식별한다.

• 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 1995년도 추계학술대회논문집; 한국종합전시장, 24 Nov. 1995
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• pp.80-85
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• 1995

Too see the effects of finite record on the estimation of WVD in practice, a window which has time varying length is examined. Its length increases linearly with time in the first half of the record, and decreases from the center of the record. The bias error due to this window decreases inversely proportionally to the window length as time increases in the first half. In the second half, the bias error increases and the resolution decreases as time increases. The bias error due to the smoothing of WVD, which is obtained by two-dimensional convolution of the true WVD and the smoothing window, which has fixed lengths along time and frequency axes, is derived for arbitrary smoothing window function. In the case of using a Gaussian window as a smoothing window, the bias error is found to be expressed as an infinite summation of differential operators. It is demonstrated that the derived formula is well applicable to the continuous WVD, but when WVD has some discontinuities, it shows the trend of the error. This is a consequence of the assumption of the derivation, that is the continuity of WVD. For windows other than Gaussian window, the derived equation is shown to be well applicable for the prediction of the bias error.