scholarly journals Biorthogonal Wavelet on a Logarithm Curve ℂ

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Xiaohui Zhou ◽  
Gang Wang
Keyword(s):  
Scaling Function ◽  
Smooth Curve ◽  
Wavelet Function ◽  
Financial Data ◽  
Discretization Method ◽  
Biorthogonal Wavelet ◽  
Numerical Application ◽  
Wavelet Filters ◽  
Euler Discretization

According to the length-preserving projection and Euler discretization method, biorthogonal wavelet function on a smooth curve C is constructed in this paper, such as a logarithm curve. The properties of biorthogonal wavelet filters on a smooth curve C are discussed, such as induced refinable equation and symmetry. Moreover, an example is given for discussing the biorthogonal scaling function and its dual on a logarithm curve C . Finally, a numerical application is given for dealing with financial data.

Wavelet transform on regression trend curve and its application in financial data

2020 ◽  
Vol 18 (05) ◽  
pp. 2050040 ◽  
Author(s):  
Xiaohui Zhou
Keyword(s):  
Wavelet Transform ◽  
Reconstruction Algorithm ◽  
Wavelet Function ◽  
Financial Data ◽  
Discrete Wavelet ◽  
Reconstruction Algorithms ◽  
Regression Curve ◽  
Growth Trend ◽  
Wavelet Filters ◽  
New Research

In this paper, wavelet transform on a regression curve is investigated by using length-preserving projection and its application in financial data is also discussed. First, properties of wavelet filters on the regression trend curves are studied and two-scale equation of wavelet function is deduced on the regression trend curves. Second, the decomposition and reconstruction algorithm of discrete wavelet transform on regression trend curves is derived. Finally, two examples in financial data are given for discussion, based on decomposition and reconstruction algorithms on regression trend curves. Some new research interpretations are presented in dealing with financial data such as “volatility on regression growth trend”, “error on regression growth trend”, and so on.

scholarly journals Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fengjuan Zhu ◽  
Qiufu Li ◽  
Yongdong Huang
Keyword(s):  
Scaling Function ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Reconstruction Algorithm ◽  
Wavelet Function ◽  
Necessary Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Numerical Examples ◽  
Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed.

scholarly journals DESIGN OF BIORTHOGONAL WAVELET FILTERS USING DYADIC LIFTING SCHEME

10.5109/12595 ◽  
2005 ◽  
Vol 37 ◽  
pp. 123-136 ◽  
Author(s):  
Turghunjan Abdukirim ◽  
Koichi Niijima ◽  
Shigeru Takano
Keyword(s):  
Lifting Scheme ◽  
Biorthogonal Wavelet ◽  
Wavelet Filters
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