Appendix E: Introduction to wavelet theory

Wavelet based image compression standards not only inspired signal and image processing community but also the research community of many research and application fields towards the wavelet theory. All wavelet based schemes follow the standard sequence of steps. They are transformation and the processing task at one end followed by the inverse of processing task and inverse transform at another end. Wavelet based compression was done in a quite different manner from its inception. The early techniques include Embedded Zerotree Wavelet (EZW) coding and Set Partitioning in Hierarchical Trees (SPIHT) coding. Although, SPIHT is an extension of EZW, both follow more or less similar process in coding and decoding. These schemes code the significant and insignificant coefficients using symbols or maintaining a list of indices of the coefficients. The decision on significant or insignificant will be taken by comparing with a threshold which will be updated in each iteration. In both the schemes, if a coefficient is identified as an insignificant one, then the bits incurred in conveying this coefficient is less and in many cases very less. One can imagine that if a coefficient is made to be an insignificant then the number of bits required will be less. This issue was taken up in this paper and bits of selected regions is chosen and a significant improvement is compression ratio is observed at a little cost of quality.

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The Time-Frequency Analysis for Energy Dissipation Shed-Tunnel’s Rockfall Impact Signal Based on Wavelet Theory

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.243-249.5085 ◽

2011 ◽

Vol 243-249 ◽

pp. 5085-5088

Author(s):

Lin Feng Wang ◽

Hong Mei Tang ◽

Hong Kai Chen

Keyword(s):

Energy Dissipation ◽

Frequency Analysis ◽

Calculation Result ◽

Signal To Noise Ratio ◽

Prevention Measures ◽

Autocorrelation Analysis ◽

Wavelet Theory ◽

Signal To Noise ◽

Time Frequency Analysis ◽

Time Frequency

Shed-tunnel is one of common prevention measures along the highway. Through the wavelet theory we denoised the rockfall impact signal when the rock impact the ordinary shed-tunnel and the energy dissipation shed-tunnel. And then we evaluated the wavelet theory’s denoise effect by the signal-to-noise ratio. The calculation result indicated that the denoise effect is very good. At last, through the autocorrelation analysis and time-frequency analysis for the rockfall impact signal, it was found that the ordinary shed-tunnel’s impact signals didn’t have obvious frequency and the frequency contained many component,but the energy dissipation shed-tunnel’s impact signals had obvious frequency. So the energy dissipation shed-tunnel’s impact signals had a relatively fixed cycle and frequency. The received frequency of rockfall impact by the time-frequency analysis could provide the basis for the design of energy dissipation shed-tunnel’s natural frequency.

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Wavelet Theory and Application Summarizing

Information Computing and Applications - Lecture Notes in Computer Science ◽

10.1007/978-3-642-25255-6_43 ◽

2011 ◽

pp. 337-343

Author(s):

Hong-yu Feng ◽

Jian-ping Wang ◽

Yan-cui Li ◽

Jun Chen

Keyword(s):

Wavelet Theory

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Wavelet Lifting Scheme for the Numerical Solution of Dynamic Reynolds Equation for Micropolar Fluid Lubrication

International Journal of Computational Methods ◽

10.1142/s021987622150033x ◽

2021 ◽

pp. 2150033

Author(s):

S. C. Shiralashetti ◽

M. H. Kantli ◽

A. B. Deshi

Keyword(s):

Numerical Solution ◽

Micropolar Fluid ◽

Reynolds Equation ◽

Lifting Scheme ◽

Computational Time ◽

Biorthogonal Wavelets ◽

Wavelet Theory ◽

Science And Engineering ◽

Promising Tool ◽

Wavelet Lifting

Recently, wavelet theory has become a well recognized promising tool in science and engineering field; especially, wavelets are successfully used in fast algorithms for easy execution. In this paper, we developed wavelet lifting scheme using orthogonal and biorthogonal wavelets for the numerical solution of dynamic Reynolds equation for micropolar fluid lubrication. The numerical results gained through proposed scheme are compared with the exact solution to expose the accuracy with speed of convergence in lesser computational time as compared with the existing methods. The examples are given to demonstrate the applicability and attractiveness of proposed method.

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