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소음진동 = Journal of KSNVE v.7 no.2, 1997년, pp.319 - 329   피인용횟수: 1

### 위그너-빌 분포함수에서의 혼신성분 저감 방법 - 회전 창문함수 A Method to Reduce the Cross-Talk of Wigner-Ville Distribution;Rotating Window

박연규    (한국과학기술원 기계공학과   ); 김양한    (한국과학기술원 기계공학과  );
• #### 초록

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.

• #### 주제어

위그너-빌 분포함수 .   앰비규이티 함수 .   혼신성분 .   스므딩 .   회전 창문함수 .   Wigner-Ville Distribution .   Ambignity Function .   Cross-talk .   Smoothing .   Rotating Window.

• #### 참고문헌 (11)

1. Time-Frequency Distribution-A Review , L. Cohen , Proceedings of the IEEE / v.77,pp.941-981,
2. Improved Time-Frequency Representation of Multicomponent Signals Using Exponential Kernels , H.-I. Choi;W.J. Williams , IEEE Trans. Acoust., Speech, Signal Processing / v.ASSP-37,pp.862-871,
3. The Wigner Distribution-A Tool for Time-Frequency Signal Analysis;Part Ⅲ:Relations with Other Time-Frequency Signal Transformations , T.A.C.M. Claasen;W.F.G. Mecklenbr$\"{a}$uker , Philips J. Res. / v.35,pp.372-389,
4. The Wigner Distribution-A Tool for Time-Frequency Signal Analysis;Part Ⅰ: Continuous-Time Signals , T.A.C.M. Claasen;W.F.G. Mecklenbr$\"{a}$uker , Philips J. Res. / v.35,pp.217-250,
5. On the Quantum Correction for Thermodynamic Equilibrium , E. Wigner , Physical Review / v.40,pp.749-759,
6. On Positivity of Time-Frequency Distribution , J.E.M. Janssen;T.A.C.M. Claasen , IEEE Trans. Acoust., Speech, Signal Processing / v.ASSP-33,pp.1029-1032,
7. WignerVille Spectral Analysis of Non-stationary Process , W. Martin;P. Flandrin , IEEE Trans. Acoust., Speech, Signal Processing / v.ASSP-33,pp.1461-1470,
8. Bias Error due to Windows for the Wigner-Ville Distribution Estimation , Y.-K. Park;Y.-H. Kim , Mechanical Systems and Signal Processing / v.9,pp.675-684,
9. A Method to Minimize the Cross-Talk of Wigner-Ville Distribution , Y.-K. Park;Y.-H. Kim , accepted for Mechanical Systems and Signal Processing / v.,pp.,
10. The Application of the Wigner Distribution to the Identification of Structure-Borne Noise Components , T.J. Wahl;J.S. Bolton , J. of Sound and Vibration / v.163,pp.101-122,
11. Wigner transforms, Gabor coefficients, and Weyl-Heisenberg wavelets , M.R. Dellomo;G.M. Jacyna , J. of Acoust. Soc. Am. / v.89,pp.2355-2361,
• #### 이 논문을 인용한 문헌 (1)

1. Choi, Young-Chul ; Park, Jin-Ho ; Yoon, Doo-Byung 2008. "Monitoring Pipe Thinning Using Two Accelerometers" 한국소음진동공학회논문집 = Transactions of the Korean society for noise and vibration engineering, 18(12): 1286~1292

저자의 다른 논문

• #### 김양한 (27)

1. 1991 "복합형 반사형 소음기의 음향학적 특성과 설계방법" 소음진동 = Journal of KSNVE 1 (1): 29~38
2. 1995 "음향 에너지, 파워, 인텐시티의 능동소음제어 방법론" 전기학회지= The Processing of the Institute of Electrical Engineers 44 (10): 40~46
3. 1997 "음향 인텐시티를 이용한 관 외부 방사 소음의 능동 제어" 소음진동 = Journal of KSNVE 7 (3): 427~437
4. 1997 "박막과 음장의 연성에 의한 저주파 소음 저감" 소음진동 = Journal of KSNVE 7 (4): 579~588
5. 1997 "회전 창문함수를 적용한 위그너-빌 분포함수와 그 특성" 소음진동 = Journal of KSNVE 7 (5): 747~756
6. 1998 "축대칭 3차원 물체의 유동 소음 스펙트럼 측정" 大韓機械學會論文集. Transactions of the Korean Society of Mechanical Engineers. B. B 22 (6): 725~733
7. 1998 "능동음원 및 벽면 어드미턴스의 재구성을 통한 실내 소음원의 정확한 규명 방법" 소음진동 = Journal of KSNVE 8 (3): 435~440
8. 1998 "성덕대왕 신종의 소리" 방송공학회지 = Korea society broadcast engineers magazine 3 (1): 28~38
9. 1998 "평면 음향 홀로그래피에서 센서간 특성 차이와 측정 위치의 부정확성에 의한 음압 추정 오차의 정량화" 소음진동 = Journal of KSNVE 8 (6): 1023~1029
10. 1999 "박막-공동계의 주파수 특성과 응용" 소음진동 = Journal of KSNVE 9 (6): 1123~1130

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