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In this paper, we propose an orthonormal wavelet basis having a dilation factor (R + 1)/ R with an arbitrary real number R > 0. This orthonormal wavelet basis requires an infinite number of wavelet shapes when the dilation factor (R + 1)/ R is ir-rational, and (R + 1)/ R can be taken an arbitrary real number greater than 1 with the appropriate real number R > 0.
In this paper, firstly, we prove a useful theorem to investigate behavior of discrete wavelet transforms in the frequency domain. Next, based on this theorem, we propose a 3-dilation orthogonal basis, constructed from two types of symmetric and antisymmetric wavelets arrayed alternately. Finally, based on this orthogonal basis, we propose a 3-dilation complex discrete wavelet transform having perfect...
In this paper, we propose a design method for directional selection in the 2-Dimensional Complex Wavelet Packet Transform. Previous 2-Dimensional Complex Discrete Wavelet Transforms break up direction components, but the number of directions is small, and the directions and resolutions are fixed. So, they are not flexible enough. In this study, we propose a new design method that can detect desirable...
Today, Virtual Reality (VR) technology has been widely applied in various fields. In past research, the influence of inducing VR in humans through the human senses or virtual effects has been studied. However the methods used to analyze human sensation have only involved measuring the center of gravity and questionnaire surveys. On the other hand, it is known that the sensation induced by VR affects...
In this study, we first analyze the characteristics of knocking and the standing-wave by the wavelet transform using the ion current waveform, which is measured in a spark-ignition engine. Based on this result, we design wavelets to detect knocking from the ion current waveform. We next define an evaluation parameter E, and apply it to knocking detection and show its effectiveness.
In the methods of video based fire detection, wavelet was usually used to test whether a pixel belongs to fire region, while fast Fourier transform was used to describe the contour of fire area. We try these two methods on images with forest flame, and develop one new approach combined both wavelet and FFT. In our method, contour of fire is found firstly, then is presented by FFT, and then temporal...
Traditional method of structural vibration control through stiffen the components, decoupling the harmonic resonance system, vibration and damping isolation, or dynamic vibration absorb, all rely structure damping consumption the energy, the control effect is limited because the constraints of materials performance. Piezoelectric smart structure with advantages such as fast response, arrangement flexible,...
Independent Component Analysis (ICA) is a useful method for blind source separation of two signals or more. We have previously proposed a new method combining ICA with the complex discrete wavelet transform (CDWT). In this case, the voice and the noise were separated using a new method. At that time, we used the simulation signal. In this study, we analyze measured biological signals by using this...
In this study, in order to improve the effectiveness of abnormal signal detection, we first develop a novel parasitic discrete wavelet transform (P-DWT) to perform fast wavelet instantaneous correlation (F-WIC) and then propose a new design method of the parasitic filters for the P-DWT. Furthermore, we show a judgment standard for assessing the credibility of the abnormal signal detection by using...
The research of dynamic stability involve some subjects, and it is a new research developed recent decades. It is very complex of its instability mechanization because of it is a nonlinear differential equation, so it has not achieve a common view. Wavelets analysis can solve many difficult problems that Fourier analysis can not solve, which has become a new bench developing rapidly in mathematical...
The CDWT was first proposed by Kingsbury as a tool for motion estimation in 1998. It was effective at solving the problem of poor translation invariance in the traditional DWT and has been applied in various fields. Thus, its practical use occurred early on, and its rationality was not theoretically interpreted. We have constructed an important base theory of the CDWT, and established a novel design...
Teeming with large-span and complex structure, it play a more and more important role in on-line monitor and diagnosis of structure health based on the advanced equipment and scientific methods. Not only the methods based on inherent frequency, or vibration mode changes, but also flexibility or stiffness changes measurement method, exist a common limitation which insufficient in the small and fatigue...
In this study, a novel direction selection method using the two dimensional complex discrete wavelet transform is proposed. In order to achieve arbitrary direction selection, direction extraction filters are designed. And then, this method is applied to the surface analysis of a wafer, and it is confirmed that our method is effective in detecting irregular direction components.
Support Vector Machines (SVM) is a new general machine-learning tool based on structural risk minimization principle. This characteristic is very signific ant for the fault diagnostics when the number of fault samples is limited. Considering that SVM theory is originally designed for a two-class classification, a hybrid SVM scheme is proposed for multi-fault classification of rotating machinery in...
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