• Journal of applied mathematics & informatics
• /
• v.4 no.2
• /
• pp.529-534
• /
• 1997

Even though the Shannon wavelet is a prototype of wavelets are assumed to have. By providing a sufficient condition to compute the size of Gibbs phe-nomenon for the Shannon wavelet series we can see the overshoot is propotional to the jump at discontinuity. By comparing it with that of the Fourier series we also that these two have exactly the same Gibbs constant.

• Communications of the Korean Mathematical Society
• /
• v.13 no.1
• /
• pp.181-193
• /
• 1998

The Shannon sampling series is the prototype of an interpolating series or sampling series. Also the Shannon wavelet is one of the protypes of wavelets. But the coefficients of the Shannon sampling series are different function values at the point of discontinuity, we analyze the Gibbs phenomenon for the Shannon sampling series. We also find a way to go around this overshoot effect.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.176-181
• /
• 2002

The continuous Gabor wavelet transform (GWT) has been utilized as a useful time-frequency analysis tool to identify the rapidly-varying characteristics of some wave signals. In the application of GWT, it is important to select the Gabor wavelet with the optimal shape factor by which the time-frequency distribution of a signal can be accurately estimated. To find the signal-dependent optimal Gabor wavelet shape factor, the notion of the Shannon entropy which mesures the extent of signal energy concentration in the time-frequency plane is employed. To verify the validity of the present entropy-based scheme, we have applied it to the time-frequency analysis of a set of elastic bending wave signals generated by an impact in a solid cylinder.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11a
• /
• pp.324.1-324
• /
• 2002

The continuous Gabor wavelet transform (GWT) has been utilized as a useful time-frequency analysis tool to identify the rapidly-varying characteristics of some wave signals. In the application of GWT, it is important to select the Gabor wavelet with the optimal shape factor by which the time-frequency distribution of a signal can be accurately estimated. To find the signal-dependent optimal Gator wavelet shape factor, the notion of the Shannon entropy which measures the extent of signal energy concentration in the time-frequency plane is employed. (omitted)

• Communications for Statistical Applications and Methods
• /
• v.9 no.1
• /
• pp.241-248
• /
• 2002

The problem of wavelet density estimation based on Shannon's wavelets is studied when the sample observations are contaminated with random noise. In this paper we will discuss the asymptotic normality for deconvolving wavelet density estimator of the unknown density f(x) when courier transform of random noise has polynomial descent.

• Proceedings of the KIEE Conference
• /
• 2011.07a
• /
• pp.2051-2052
• /
• 2011

The structural defects of a heart often reflects the sounds that the heart produces. This paper describes heart sound analysis method using Wavelet transform and average Shannon energy. This can extract the features of heart sounds in various disease identify the heart sounds. Experimental results show that the presented method has potential application in detecting various heart diseases.

• Proceedings of the Safety Management and Science Conference
• /
• 2001.11a
• /
• pp.91-97
• /
• 2001

본 연구는 Fourier, Shannon, Gabor, Wavelet Filters 간의 상호비교를 통해 Wavelet Analysis의 장점을 도출하고 학제간 모든 과학기술에 적용될 수 있는 분야를 유형화하고 기존 연구를 고찰한다.

• Smart Structures and Systems
• /
• v.18 no.5
• /
• pp.1063-1085
• /
• 2016

Taking advantage of the high sensitivity and long-distance detection capability of acoustic emission (AE) technique, this paper focuses on the crack detection in rail head, which is one of the most vulnerable parts of rail track. The AE source location and noise cancellation were studied on the basis of practical rail profile, material and operational noise. In order to simulate the actual AE events of rail head cracks, field tests were carried out to acquire the AE waves induced by pencil lead break (PLB) and operational noise of the railway system. Wavelet transform (WT) was first utilized to investigate the time-frequency characteristics and dispersion phenomena of AE waves. Here, the optimal mother wavelet was selected by minimizing the Shannon entropy of wavelet coefficients. Regarding the obvious dispersion of AE waves propagating along the rail head and the high operational noise, the wavelet transform-based modal analysis location (WTMAL) method was then proposed to locate the AE sources (i.e. simulated cracks) respectively for the PLB-induced AE signals with and without operational noise. For those AE signals inundated with operational noise, the Hilbert transform (HT)-based noise cancellation method was employed to improve the signal-to-noise ratio (SNR). Finally, the experimental results demonstrated that the proposed crack detection strategy could locate PLB-simulated AE sources effectively in the rail head even at high operational noise level, highlighting its potential for field application.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.36 no.7
• /
• pp.813-822
• /
• 2012

Abnormal operating sounds radiated from a moving transfer robot in LCD (liquid crystal display) product lines have been used for the fault detection line of a robot instead of other source signals such as vibrations, acoustic emissions, and electrical signals. Its advantage as a source signal makes it possible to monitor the status of multiple faults by using only a microphone, despite a relatively low sensitivity. The wavelet packet transform for feature extraction and the artificial neural network for fault classification are employed. It can be observed that the abnormal operating sound is sufficiently useful as a source signal for the fault diagnosis of mechanical components as well as other source signals.

• Smart Structures and Systems
• /
• v.8 no.3
• /
• pp.303-320
• /
• 2011

Comparing to active damage monitoring, impact localization on composite by using time reversal focusing method has several difficulties. First, the transfer function of the actuator-sensor path is difficult to be obtained because of the limitation that no impact experiment is permitted to perform on the real structure and the difficulty to model it because the performance of real aircraft composite is much more complicated comparing to metal structure. Second, the position of impact is unknown and can not be controlled as the excitation signal used in the active monitoring. This makes it not applicable to compare the difference between the excitation and the focused signal. Another difficulty is that impact signal is frequency broadband, giving rise to the difficulty to process virtual synthesis because of the highly dispersion nature of frequency broadband Lamb wave in plate-like structure. Aiming at developing a practical method for on-line localization of impact on aircraft composite structure which can take advantage of time reversal focusing and does not rely on the transfer function, a PZT sensor array based phase synthesis time reversal impact imaging method is proposed. The complex Shannon wavelet transform is presented to extract the frequency narrow-band signals from the impact responded signals of PZT sensors. A phase synthesis process of the frequency narrow-band signals is implemented to search the time reversal focusing position on the structure which represents the impact position. Evaluation experiments on a carbon fiber composite structure show that the proposed method realizes the impact imaging and localization with an error less than 1.5 cm. Discussion of the influence of velocity errors and measurement noise is also given in detail.