scholarly journals Besov-Hankel norms in terms of the continuous Bessel wavelet transform

2021 ◽  
Author(s):  
Ashish Pathak ◽  
Dileep Kumar
Keyword(s):  
Wavelet Transform ◽  
Wavelet Coefficient ◽  
Inversion Formulas ◽  
And Inversion

Using the theory of continuous Bessel wavelet transform in $L^2 (\mathbb{R})$-spaces, we established the Parseval and inversion formulas for the $L^{p,\sigma}(\mathbb{R}^+)$- spaces. We investigate continuity and boundedness properties of Bessel wavelet transform in Besov-Hankel spaces. Our main results: are the characterization of Besov-Hankel spaces by using continuous Bessel wavelet coefficient.

Trial Study on Methods of Damage Extent Identification Based on Wavelet Transform of Strain Signal

2010 ◽  
Vol 163-167 ◽  
pp. 2543-2548
Author(s):  
Jin Fan ◽  
Hong Po Liu
Keyword(s):  
Wavelet Transform ◽  
Wavelet Coefficient ◽  
Maximum Modulus ◽  
Steel Beam ◽  
Simply Supported ◽  
Relative Damage ◽  
Damage Extent ◽  
Strain Signal

Wavelet transform of strain signal can be used in the damage relative damage extent identification. The proposed method is validated by trial on a simply supported steel beam. And meanwhile the relative damage extent can be identified by drawing the curve of the maximum modulus of the wavelet coefficient and damage extent.

A Feature Extracting Method for Chinese Character Recognition of License Plate Based on Elastic Mesh and Wavelet Transform

2013 ◽  
Vol 760-762 ◽  
pp. 1452-1456
Author(s):  
Chao Zheng ◽  
Hua Yang ◽  
Xing Yang ◽  
Chao Chao Huang ◽  
Xiao Di Wu
Keyword(s):  
Wavelet Transform ◽  
Character Recognition ◽  
Chinese Character ◽  
Wavelet Coefficient ◽  
Difficult Problem ◽  
License Plate ◽  
Structure Information ◽  
Feature Extracting ◽  
Chinese Character Recognition ◽  
Character Feature

Low-resolution Chinese character recognition of license plate is always a difficult problem. For solving it, we must think about the distinctiveness of character feature and the counting speed of method simultaneously. In this paper, we proposed a simple and effective feature extraction algorithm. First, extract the statistical feature of Chinese character based on decomposing stroke with wavelet transform. Second, apply Elastic Mesh Algorithm into extracting wavelet coefficient of decomposing stroke to get the structure information of Chinese character. The experimental results show the method is robust against low quality Chinese characters, such as skew, fuzzy, glue, distorted character, and easy to be used in actual projects with simple advantage.

CHARACTERIZATION OF IMAGE SPACE OF A WAVELET TRANSFORM

2006 ◽  
Vol 04 (03) ◽  
pp. 547-557 ◽  
Author(s):  
CAIXIA DENG ◽  
YULING QU ◽  
LIJUAN GU
Keyword(s):  
Wavelet Transform ◽  
Truncation Error ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Sampling Theorem ◽  
Image Space ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Scope Of Application

In this paper, Journe wavelet function is introduced as a wavelet generating function. The expression of reproducing kernel function for the image space of this wavelet transform is obtained based on the fact that the image space of the wavelet transform is a reproducing kernel Hilbert space. Then the isometric identity of Journe wavelet transform is obtained. The connections between the image space of the wavelet transform and the image space of the known reproducing kernel space are established by the theories of reproducing kernel. The properties and the structures of the image space of the wavelet transform can be characterized by the properties and the structures of the image space of the known reproducing kernel space. Using the ideas of reproducing kernel, we consider there are relations between the wavelet transform and the sampling theorem. Meanwhile, the approximations in sampling theorems is shown and the truncation error is given. This provides a theoretical basis for us to study the image space of the general wavelet transform and broadens the scope of application of theories of the reproducing kernel space.

Aeroacoustic analysis of slat tones

2021 ◽  
Vol 263 (1) ◽  
pp. 5650-5663
Author(s):  
Hasan Kamliya Jawahar ◽  
Syamir Alihan Showkat Ali ◽  
Mahdi Azarpeyvand
Keyword(s):  
Wavelet Transform ◽  
Surface Pressure ◽  
Wavelet Coefficient ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Stream Velocity ◽  
High Lift ◽  
Unsteady Surface Pressure ◽  
Slat Noise ◽  
Generation Mechanisms

Experimental measurements were carried out to assess the aeroacoustic characteristics of a 30P30N high-lift device, with particular attention to slat tonal noise. Three different types of slat modifications, namely slat cove filler, serrated slat cusp, and slat finlets have been experimentally examined. The results are presented for an angle of attack of α = 18 at a free-stream velocity of U = 30 m/s, which corresponds to a chord-based Reynolds number of Re = 7 x 10. The unsteady surface pressure near the slat region and far-field noise were made simultaneously to gain a deeper understanding of the slat noise generation mechanisms. The nature of the low-frequency broadband hump and the slat tones were investigated using higher-order statistical approaches for the baseline 30P30N and modified slat configurations. Continuous wavelet transform of the unsteady surface pressure fluctuations along with secondary wavelet transform of the broadband hump and tones were carried out to analyze the intermittent events induced by the tone generating resonant mechanisms. Stochastic analysis of the wavelet coefficient modulus of the surface pressure fluctuations was also carried out to demonstrate the inherent differences of different tonal frequencies. An understanding into the nature of the noise generated from the slat will help design the new generation of quite high-lift devices.

Digital Watermarking for 3D Polygonal Model Based on Wavelet Transform

1999 ◽  
Author(s):  
Hiroaki Date ◽  
Satoshi Kanai ◽  
Takeshi Kishinami
Keyword(s):  
Wavelet Transform ◽  
Digital Watermarking ◽  
Copyright Protection ◽  
Affine Transformation ◽  
Wavelet Coefficient ◽  
Original Data ◽  
Geometric Error ◽  
Digital Data ◽  
Cad Cam ◽  
Polygonal Model

Abstract Recently, much interest is being taken in a method to protect the copyright of digital data and prevent illegal duplication of it. However, in the area of CAD/CAM and CG, there are no effective ways to protect the copyright of the 3D geometric models. As a first step to solve this problem, a new digital watermarking method for 3D polygonal models is introduced in this paper. Watermarking is one of the copyright protection methods where an invisible watermark is secretly embedded into the original data. The proposed watermarking method is based on the wavelet transform (WT) and multi-resolution representation (MRR) of the polygonal model. The watermark can be embedded in the large wavelet coefficient vectors at various resolution levels of the MRR. This makes the embedded watermark imperceptible and invariant to the affine transformation, and also makes the control of the geometric error caused by the watermarking reliable.

The Meaning of Wavelet Transform in High Resolution Sequence Stratigraphy Study

2013 ◽  
Vol 411-414 ◽  
pp. 3035-3038
Author(s):  
Zhan Dong Li ◽  
Meng Li ◽  
Yan Liu
Keyword(s):  
Wavelet Transform ◽  
High Resolution ◽  
Sequence Stratigraphy ◽  
Wavelet Coefficient ◽  
Scale Factor ◽  
Sequence Stratigraphic ◽  
Natural Gamma ◽  
Set Up ◽  
Morlet Wavelet Transform ◽  
High Resolution Sequence Stratigraphy

Taking the division of Gao3 reservoir group strata sequence in Songliao basin of Daqing Changyuan Xingbei for example, this paper analyzed the applicability of the one-dimensional continuous wavelet transform in high resolution sequence division. By means of making morlet wavelet transform on the natural gamma logging curve, the connection between well curve signal and depth is transformed to the alter relationship between depth and the domains of scale, which obtains the wavelet coefficient curve. Then set up the corresponding relations between periodic oscillations characteristics of wavelet coefficient curve and sequence interface at all levels under the optimal scale factor. And the wavelet coefficients curve in best scale factor will eventually be used for the identification and division of the sequence. Practice has proved that the wavelet coefficient curve in the best factor can accurately identify the sequence interface at all levels, and the result is more accurate, objective and effective than manual calibration. So take advantage of wavelet transform in sequence stratigraphic classification provides a new way for high resolution sequence stratigraphy studies.

A Local Multiscale Characterization of Edges Applying the Wavelet Transform

1998 ◽  
pp. 261-277
Author(s):  
Carl J. G. Evertsz ◽  
Kathrin Berkner ◽  
Wilhelm Berghorn
Keyword(s):  
Wavelet Transform

scholarly journals Time-space characterization of droughts in the São Francisco river catchment using the Standard Precipitation Index and continuous wavelet transform

RBRH ◽  
2019 ◽  
Vol 24 ◽  
Author(s):  
Marcus Suassuna Santos ◽  
Veber Afonso Figueiredo Costa ◽  
Wilson dos Santos Fernandes ◽  
Rafael Pedrollo de Paes
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Large Scale ◽  
Continuous Wavelet ◽  
River Catchment ◽  
Time Space ◽  
L Moments ◽  
Space Characterization

ABSTRACT This paper focuses on time-space characterization of drought conditions in the São Francisco River catchment, on the basis of wavelet analysis of Standardized Precipitation Index (SPI) time series. In order to improve SPI estimation, the procedures for regional analysis with L-moments were employed for defining statistically homogeneous regions. The continuous wavelet transform was then utilized for extracting time-frequency information from the resulting SPI time series in a multiresolution framework and for investigating possible teleconnections of these signals with those obtained from samples of the large-scale climate indexes ENSO and PDO. The use of regional frequency analysis with L-moments resulted in improvements in the estimation of SPI time series. It was observed that by aggregating regional information more reliable estimates of low frequency rainfall amounts were obtained. The wavelet analysis of climate indexes suggests that the more extreme dry periods in the study area are observed when the cold phase of both ENSO and the PDO coincides. While not constituting a strict cause effect relationship, it was clear that the more extreme droughts are consistently observed in this situation. However, further investigation is necessary for identifying particularities in rainfall patterns that are not associated to large-scale climate anomalies.

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