scholarly journals Isolation of a periodic component by singular wavelet decomposition

2020 ◽  
pp. 4-8
Author(s):  
V. M. Romanchak ◽  
M. A. Hundzina
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Wavelet Decomposition ◽  
Periodic Component ◽  
Discrete Wavelet ◽  
Real Problem ◽  
Wavelet Method ◽  
Parametric Regression ◽  
Validity Condition ◽  
Wavelet Transformations

In this paper, we propose to use a discrete wavelet transform with a singular wavelet to isolate the periodic component from the signal. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet is zero). For singular wavelets, the validity condition is not met. As a singular wavelet, you can use the Delta-shaped functions, which are involved in the estimates of Parzen-Rosenblatt, Nadaraya-Watson. Using singular value of a wavelet is determined by the discrete wavelet transform. This transformation was studied earlier for the continuous case. Theoretical estimates of the convergence rate of the sum of wavelet transformations were obtained; various variants were proposed and a theoretical justification was given for the use of the singular wavelet method; sufficient conditions for uniform convergence of the sum of wavelet transformations were formulated. It is shown that the wavelet transform can be used to solve the problem of nonparametric approximation of the function. Singular wavelet decomposition is a new method and there are currently no examples of its application to solving applied problems. This paper analyzes the possibilities of the singular wavelet method. It is assumed that in some cases a slow and fast component can be distinguished from the signal, and this hypothesis is confirmed by the numerical solution of the real problem. A similar analysis is performed using a parametric regression equation, which allows you to select the periodic component of the signal. Comparison of the calculation results confirms that nonparametric approximation based on singular wavelets and the application of parametric regression can lead to similar results.

scholarly journals Detecting the Fluctuations in Large Samples Using Wavelet Transform

2018 ◽  
Vol 12 (12) ◽  
pp. 245
Author(s):  
S. AL Wadi ◽  
Ghassan Obeidat
Keyword(s):  
Wavelet Transform ◽  
Data Analysis ◽  
Stock Market ◽  
Discrete Wavelet Transform ◽  
The Other ◽  
Discrete Wavelet ◽  
Wavelet Method ◽  
Market Data ◽  
Large Samples ◽  
The Government

structure break is a famous features in stock market data that gain consideration from many kind of researchers. Generally, it occurs because of unexpected variations in the strategy of the government. Recently, wavelet method (WT) is more popular in the stock market data analysis since it has significant benefits than the other traditional methods. In this research paper, the discrete wavelet transform (DWT) based on Daubechies model will be used to capture the structure break in Amman stocks market /Jordan (ASE) using dataset from 2010 until 2018.

scholarly journals Diagnosis of Encephalopathy Based on Energies of EEG Subbands Using Discrete Wavelet Transform and Support Vector Machine

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jisu Elsa Jacob ◽  
Gopakumar Kuttappan Nair ◽  
Thomas Iype ◽  
Ajith Cherian
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Wavelet Decomposition ◽  
Support Vector ◽  
Svm Classifier ◽  
Discrete Wavelet ◽  
Eeg Analysis ◽  
Biomedical Signal ◽  
Time Frequency ◽  
Frequency Domain Methods

EEG analysis in the field of neurology is customarily done using frequency domain methods like fast Fourier transform. A complex biomedical signal such as EEG is best analysed using a time-frequency algorithm. Wavelet decomposition based analysis is a relatively novel area in EEG analysis and for extracting its subbands. This work aims at exploring the use of discrete wavelet transform for extracting EEG subbands in encephalopathy. The subband energies were then calculated and given as feature sets to SVM classifier for identifying cases of encephalopathy from normal healthy subjects. Out of various combinations of subband energies, energy of delta subband yielded highest performance parameters for SVM classifier with an accuracy of 90.4% in identifying encephalopathy cases.

scholarly journals Digital watermarking algorithm based on 4-level discrete wavelet transform and discrete fractional angular transform

2021 ◽  
Vol 51 (4) ◽  
Author(s):  
Jing-You Li ◽  
Chun-Hui Zhao ◽  
Guang-Da Zhang
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Digital Watermarking ◽  
Wavelet Decomposition ◽  
Optical Bistability ◽  
Discrete Wavelet ◽  
Medium Frequency ◽  
Geometric Transformations ◽  
Transform Coefficients ◽  
Point Detection

Nowadays, there are many watermarking algorithms based on wavelet transform. The simple one is to insert directly the watermark into the wavelet transform coefficients. However, most of the existing watermarking schemes can only resist traditional signal processing attacks, such as image compression, noise and filtering. When the watermarked image is subject to geometric transformations, especially rotation attack, it is hard to detect the watermark successfully. In this paper, a digital watermarking algorithm is proposed based on 4-level discrete wavelet transform and discrete fractional angular transform. To enhance the security of the algorithm, the watermark is scrambled with the simplicity of Arnold transform and chaos-based mix optical bistability model, since the chaos is pseudorandom and sensitive to the initial values. And the watermark is embedded into the medium frequency sub-band of the 1-level wavelet decomposition according to the Harris feature point detection. Simulation results show that the proposed digital watermarking algorithm by combining 4-level discrete wavelet transform with discrete fractional angular transform could resist rotation attack and other common attacks.

Improving Space Localization Properties of the Discrete Wavelet Transform

Informatica ◽  
2013 ◽  
Vol 24 (4) ◽  
pp. 657-675
Author(s):  
Jonas Valantinas ◽  
Deividas Kančelkis ◽  
Rokas Valantinas ◽  
Gintarė Viščiūtė
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Discrete Wavelet ◽  
Space Localization

An Adaptive Binarization Method for Cost-efficient Document Image System in Wavelet Domain

2020 ◽  
Vol 64 (3) ◽  
pp. 30401-1-30401-14 ◽  
Author(s):  
Chih-Hsien Hsia ◽  
Ting-Yu Lin ◽  
Jen-Shiun Chiang
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Document Image ◽  
Background Information ◽  
Raspberry Pi ◽  
Discrete Wavelet ◽  
Image System ◽  
Low Frequencies ◽  
Cost Efficient ◽  
Binarization Method

Abstract In recent years, the preservation of handwritten historical documents and scripts archived by digitized images has been gradually emphasized. However, the selection of different thicknesses of the paper for printing or writing is likely to make the content of the back page seep into the front page. In order to solve this, a cost-efficient document image system is proposed. In this system, the authors use Adaptive Directional Lifting-Based Discrete Wavelet Transform to transform image data from spatial domain to frequency domain and perform on high and low frequencies, respectively. For low frequencies, the authors use local threshold to remove most background information. For high frequencies, they use modified Least Mean Square training algorithm to produce a unique weighted mask and perform convolution on original frequency, respectively. Afterward, Inverse Adaptive Directional Lifting-Based Discrete Wavelet Transform is performed to reconstruct the four subband images to a resulting image with original size. Finally, a global binarization method, Otsu’s method, is applied to transform a gray scale image to a binary image as the output result. The results show that the difference in operation time of this work between a personal computer (PC) and Raspberry Pi is little. Therefore, the proposed cost-efficient document image system which performed on Raspberry Pi embedded platform has the same performance and obtains the same results as those performed on a PC.

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