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Suppress the Finger Reflection Error of Littlewood-pelay Wavelet Transformation Device of Surface Acoustic Wave  [cached]
Li Yuanyuan,Chen Guangjie,Liu Junyu
Research Journal of Applied Sciences, Engineering and Technology , 2013,
Abstract: In this study, a Wavelet Transformation (WT) device of Surface Acoustic Wave (SAW) technology is developed on the basis of acoustics, electronics, wavelet theory, applied mathematics and semiconductor planar technology. The Finger Reflection (FR) error is the primary reason for this kind of device. To solve the problem, a mathematic model of Littlewood-pelay wavelet was established first, which is matched with the model of SAW. Using the methods of split finger and fake finger to design IDT of Littlewood-pelay WT device of SAW with L-edit software, the FR error can be reduced and the equivalent construction of IDT is simulated.
PCB image mosaics algorithm based on wavelet transformation and phase correlation

LAI Yu-feng,CHENG Liang-lun,

计算机应用研究 , 2009,
Abstract: In order to stitch images captured by camera into an entire one, this paper developed an image mosaic method. Traditional image mosaics algorithms did not work well on AOI because of optical noise and complexity. It used two-dimensio-nal wavelet transformation to get the high frequency coefficients that reflected the changes of image in horizontal and vertical direction, at the same time it removed the low coefficients that reflected the gradual changes of illumination and reduced the computational complexity. Then the algorithm used phase correlation technology to determine the location of the overlap, and achieved image fusion by weighted average method. The proposed algorithm was tested by experiments and worked well.
The continuous fractional Bessel wavelet transformation
Akhilesh Prasad, Ashutosh Mahato, V. K. Singh and M. M. Dixit
Boundary Value Problems , 2013, DOI: 10.1186/1687-2770-2013-40
Abstract: The main objective of this paper is to study the fractional Hankel transformation $(FrHT)$ and its some basic properties. Applications of the $FrHT$ in solving generalized $n^{th}$ order linear nonhomogeneous ordinary differential equations are given. The continuous fractional Bessel wavelet transformation, its inversion formula, and the Parseval's relation for continuous fractional Bessel wavelet transformation are also studied.
The Automatic Recognition of Human Faces Based on the Uncorrelated Optimal Discriminant Transformation and Multiclassifier Combination

ZHAO Hai-tao,JIN Zhong,YANG Jing-yu,
,金 忠,杨静宇

中国图象图形学报 , 2000,
Abstract: Face recognition technology(FRT) has numerous commercial and law enforcement applications, especially in video surveillance. The primary task at hand, given still or video images, requires the identification of one or more persons using a database of stored face images. Based on Fisher discriminant criterion, In order to extract features by using the uncorrelated discriminant transformation, we use orthogonal wavelet transformation and KL transformation to process the face images at first. According to peoples' recognition experience, we use multi feature and multi classifier combination to give out the classification results. Experiments on ORL database obtained an error rate of 2%, which is the best result on this database up to now. Experimental results also show that this method does not sensitive to the pose and expression of human faces.
Object Edge Smoothing by Wavelet Transformation  [PDF]
Zheng Xiaodong,Huang Xinghan,Wang Ming
Information Technology Journal , 2005,
Abstract: In order to solve problem that most 2D (Two-dimensional) shape representations don’t fit for wavelet transformation processing, a new method of 2D shape representation has been put forward. It stores object borderline pixels coordinate value (xi, yi) into two arrays x = X[i]; y = Y[i] by the sequence of object borderline tracking result, object boundary has been represented by this two array. It changes a 2D image problem into two single dimension arrays’ problem and can be processed by wavelet transformation. Then make full use of the ability of time and frequency localization of wavelet transformation and find characters both in time and frequency. The boundaries leaps can be distinguish from noise. This technique has been applied in workpiece boundary noise reducing. And it shows that noise can be eliminated and boundaries corners are remained at same time.
Estimates of Approximation Error by Legendre Wavelet  [PDF]
Xiaoyang Zheng, Zhengyuan Wei
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.77063
Abstract: This paper first introduces Legendre wavelet bases and derives their rich properties. Then these properties are applied to estimation of approximation error upper bounded in spaces \"\"?and \"\"?by norms \"\"?and \"\"?, respectively. These estimate results are valuable to solve integral-differential equations by Legendre wavelet method.
Entangled Husimi distribution and Complex Wavelet transformation  [PDF]
Li-yun Hu,Hong-yi Fan
Physics , 2009, DOI: 10.1007/s10773-010-0285-6
Abstract: Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.
Multiplicative Propagation of Error During Recursive Wavelet Estimation  [PDF]
Michael A. Cohen,Can Ozan Tan
Statistics , 2011,
Abstract: Wavelet coefficients are estimated recursively at progressively coarser scales recursively. As a result, the estimation is prone to multiplicative propagation of truncation errors due to quantization and round-off at each stage. Yet, the influence of this propagation on wavelet filter output has not been explored systematically. Through numerical error analysis of a simple, generic sub-band coding scheme with a half-band low pass finite impulse-response filter for down sampling, we show that truncation error in estimated wavelet filter coefficients can quickly reach unacceptable levels, and may render the results unreliable especially at coarser scales.
Error Estimation of an Approximation in a Wavelet Collocation Method
Journal of Applied Computer Science & Mathematics , 2013,
Abstract: This article describes possibility to assess anapproximation in a wavelet collocation method. In a researchproject several different types of differential equations wereapproximated with this method. A lot of parameters must beadjusted in the discussed method here, like the number of basiselements, the resolution parameter j or the number ofcollocation points. In this article we define a criterion whichfollows from an error estimation of the approximation.
Asymptotic expansion of the wavelet transform with error term  [PDF]
R S Pathak,Ashish Pathak
Mathematics , 2014,
Abstract: UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
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