scholarly journals On Generalized Carleson Operators of Periodic Wavelet Packet Expansions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shyam Lal ◽  
Manoj Kumar
Keyword(s):  
Wavelet Packet ◽  
Wavelet Packets ◽  
Arithmetic Means ◽  
Periodic Wavelet

Three new theorems based on the generalized Carleson operators for the periodic Walsh-type wavelet packets have been established. An application of these theorems as convergence a.e. for the periodic Walsh-type wavelet packet expansion of block function with the help of summation by arithmetic means has been studied.

CONSTRUCTING MULTIPLE WAVELET PACKETS WITH FIFS

Fractals ◽  
2001 ◽  
Vol 09 (02) ◽  
pp. 165-169
Author(s):  
GANG CHEN ◽  
ZHIGANG FENG
Keyword(s):  
Multiresolution Analysis ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Scaling Functions ◽  
Wavelet Packet Decomposition ◽  
Fractal Interpolation ◽  
Fractal Interpolation Functions ◽  
Interpolation Functions

By using fractal interpolation functions (FIF), a family of multiple wavelet packets is constructed in this paper. The first part of the paper deals with the equidistant fractal interpolation on interval [0, 1]; next, the proof that scaling functions ϕ1, ϕ2,…,ϕr constructed with FIF can generate a multiresolution analysis of L2(R) is shown; finally, the direct wavelet and wavelet packet decomposition in L2(R) are given.

scholarly journals Minimization of Harmonics Noise Using Wavelet Transformation Technology

2011 ◽  
pp. 216-223
Author(s):  
Mr. Debasis Dash ◽  
Mr. Shatyaprakasha Satapathy ◽  
Dr. Chittaranjan Panda
Keyword(s):  
Wavelet Analysis ◽  
Wavelet Packet ◽  
Statistical Significance ◽  
Audio Signal ◽  
Design Procedure ◽  
Wavelet Packets ◽  
Threshold Function ◽  
Analysis Tool ◽  
Real Time Processing ◽  
Wavelet Spectra

The field programmable gate array technology can design high performance system at low cost for wavelet analysis. Wavelet transform has gained the reputation of being a very effective signal analysis tool for much practical application. Implementation of transform needs the meeting of real-time processing for most application. The objectives of this paper are to compare the Haar and Daubeches technology and to calculate the bit error rate (BER) between the input audio signal and reconstructed output signal. It is seen that the BER using Daubechies wavelet technology is less than Haar wavelet. The design procedure is explained using the stat of art electronic design. Automation tools for system design on FPGA, simulation, synthesis and implementation on the FPGA technology has been carried out. The power hovmoller, cross wavelet spectra and coherence are described. A Practical step-up-step guide to wavelet analysis is given with examples taken from time series. The guide includes a comparison to the windowed Fourier transform. New statistical significance test for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise. Empirical formula is given for the effect of smoothing on significance levels and filtering. The notion of orthogonal no separable trivet wavelet packets, which is the generation of orthogonal university wavelet packets is introduced. A de-noising method based on wavelet packet shrinkage is developed. The principle of wavelet packet shrinkage for de-noising and the section of thresholds and threshold function are analyzed.

The Energy Distribution of Tire-Road Noise and Noisy Speech Based on Wavelet Packet

2011 ◽  
Vol 464 ◽  
pp. 721-724 ◽  
Author(s):  
Zhi Yong He ◽  
Li Heng Luo
Keyword(s):  
Energy Distribution ◽  
Speech Enhancement ◽  
Mobile Communications ◽  
Wavelet Packet ◽  
Noise Signal ◽  
Wavelet Packets ◽  
Road Noise ◽  
Noisy Speech ◽  
Time Frequency ◽  
The Difference

Speech enhancement is very important for mobile communications or some other applications in car. The energy distribution of signal is the basis of algorithms which denoise noisy speech in time-frequency domain. In this work, the noise regarded is the tire-road noise when driving in expressway. Wavelet packets transform is used in the analysis. After decomposing noise signal and noisy speech signal by wavelet packet transform, the analysis for the difference of the energy distribution between noisy speech and noise is finished.

A New Method for Real-Time Tool Condition Monitoring in Transfer Machining Stations1

2000 ◽  
Vol 123 (2) ◽  
pp. 339-347 ◽  
Author(s):  
Ya Wu ◽  
Philippe Escande ◽  
R. Du
Keyword(s):  
Decision Making ◽  
Condition Monitoring ◽  
Wavelet Packet ◽  
Signal Reconstruction ◽  
Spindle Motor ◽  
Tool Condition Monitoring ◽  
New Method ◽  
Wavelet Packets ◽  
Tool Condition ◽  
Threshold Crossing

This paper introduces a new method for tool condition monitoring in transfer machining stations. The new method is developed based on a combination of wavelet transform, signal reconstruction, and the probability of threshold crossing. It consists of two parts: training and decision making. Training is aimed at determining the alarm threshold and it is done in six steps: (1) Calculate the wavelet packet transform of the sensor signals (spindle motor current) obtained from normal tool conditions. (2) Select feature wavelet packets that represent the principal components of the signals. (3) Reconstruct the signals from the feature wavelet packets (this removes the unwanted noises). (4) Calculate the statistics of the reconstructed signals. (5) Calculate the alarm thresholds based on the statistics of the reconstructed signals, and (6) Calculate the probability of the threshold crossing (the number of threshold crossing conforms a Poisson distribution). The decision making is done in two steps: (1) Check the threshold crossing, and (2) Calculate the number of threshold crossing to determine whether an alarm shall be given. As demonstrated using a practical example from a drilling transfer station, the new method is effective with a success rate over 90 percent. Also, it is fast (the monitoring decision can be done in milliseconds) and cost-effective (the implementation cost shall be less than $500).

scholarly journals Chatter Detection in Milling Process Based on the Combination of Wavelet Packet Transform and PSO-SVM

2021 ◽  
Author(s):  
Qingzhen Zheng ◽  
Guangsheng Chen ◽  
Anling Jiao
Keyword(s):  
Wavelet Packet ◽  
Dimensional Accuracy ◽  
Vibration Signal ◽  
Pso Algorithm ◽  
Milling Process ◽  
Wavelet Packet Transform ◽  
Wavelet Packets ◽  
Limiting Factor ◽  
Novel Method ◽  
Traditional Approaches

Abstract Chatter has become the mainly limiting factor in the development of rapid and stable machining of machine tools, which seriously impacts on surface quality and dimensional accuracy of the finished workpiece. In this paper, a novel method of chatter recognition was proposed based on the combination of wavelet packet transform (WPT) and PSO-SVM in milling. The collected vibration signal was pre-processed by wavelet packet transform (WPT), and the wavelet packets with rich chatter information were selected and reconstructed. The selected wavelet packets can reduce the redundant noise and useless information. a combination of 10 time-domain and 4 frequency-domain feature parameters were obtained through calculating the reconstructed vibration signals. Compared to three methods of k-fold cross validation (k-CV), genetic algorithm (GA) and particle swarm optimization (PSO) to optimize the input parameters of SVM, the experiment results were shown that the PSO algorithm has is characterized by high accuracy. The proposed approach can recognize the stable, chatter and transition states more accurately than the other traditional approaches.

THE DESIGN OF COMPLEX WAVELET PACKET TRANSFORMS BASED ON PERFECT TRANSLATION INVARIANCE THEOREMS

2010 ◽  
Vol 08 (04) ◽  
pp. 537-558 ◽  
Author(s):  
HIROSHI TODA ◽  
ZHONG ZHANG ◽  
TAKASHI IMAMURA
Keyword(s):  
Wavelet Transforms ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Discrete Wavelet Transforms ◽  
Wide Range ◽  
Different Shapes ◽  
Complex Wavelet ◽  
Meyer Wavelet

The useful theorems for achieving perfect translation invariance have already been proved, and based on these theorems, dual-tree complex discrete wavelet transforms with perfect translation invariance have been proposed. However, due to the complication of frequency divisions with wavelet packets, it is difficult to design complex wavelet packet transforms with perfect translation invariance. In this paper, based on the aforementioned theorems, novel complex wavelet packet transforms are designed to achieve perfect translation invariance. These complex wavelet packet transforms are based on the Meyer wavelet, which has the important characteristic of possessing a wide range of shapes. In this paper, two types of complex wavelet packet transforms are designed with the optimized Meyer wavelet. One of them is based on a single Meyer wavelet and the other is based on a number of different shapes of the Meyer wavelets to create good localization of wavelet packets.

The Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets

2010 ◽  
Vol 439-440 ◽  
pp. 896-901
Author(s):  
Qing Jiang Chen ◽  
Yu Ying Wang
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Novel Method ◽  
Popular Subject ◽  
Vector Valued ◽  
Orthogonal Frame

Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an integer-valued dilation matrix. A novel method for constructing multi-dimen- -sional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are established. Orthogonality decomposition relation formulas of the space are derived by constructing a series of subspaces of wavelet packets. Finally, one new orthonormal wavelet packet bases of are constructed from these wavelet packets.

Testing for detection of crack in rotor using vibration analysis: an experimental approach

2019 ◽  
Vol 36 (6) ◽  
pp. 999-1013
Author(s):  
Bhumi Ankit Shah ◽  
Dipak P. Vakharia
Keyword(s):  
Condition Monitoring ◽  
Vibration Analysis ◽  
Critical Speed ◽  
Energy Analysis ◽  
Wavelet Packet ◽  
Rotating Machinery ◽  
Wavelet Packets ◽  
Energy Component ◽  
Content Type ◽  
Analysis Technique

Purpose Many incidents of rotor failures are reported due to the development and propagation of the crack. Condition monitoring is adopted for the identification of symptoms of the crack at very early stage in the rotating machinery. Identification requires a reliable and accurate vibration analysis technique for achieving the objective of the study. The purpose of this paper is to detect the crack in the rotating machinery by measuring vibration parameters at different measurement locations. Design/methodology/approach Two different types of cracks were simulated in these experiments. Experiments were conducted using healthy shaft, crack simulated shaft and glued shaft with and without added unbalance to observe the changes in vibration pattern, magnitude and phase. Deviation in vibration response allows the identification of crack and its location. Initial data were acquired in the form of time waveform. Run-up and coast-down measurements were taken to find the critical speed. The wavelet packet energy analysis technique was used to get better localization in time and frequency zone. Findings The presence of crack changes the dynamic behavior of the rotor. 1× and 2× harmonic components for steady-state test and critical speed for transient test are important parameters in condition monitoring to detect the crack. To separate the 1× and 2× harmonic component in the different wavelet packets, original signal is decomposed in nine levels. Wavelet packet energy analysis is carried out to find the intensity of the signal due to simulated crack. Originality/value Original signals obtained from the experiment test set up may contain noise component and dominant frequency components other than the crack. Wavelet packets contain the crack-related information that are identified and separated in this study. This technique develops the condition monitoring procedure more specific about the type of the fault and accurate due to the separation of specific fault features in different wavelet packets. From the experiment end results, it is found that there is significant rise in a 2× energy component due to crack in the shaft. The intensity of a 1× energy component depends upon the shaft crack and unbalance orientation angle.

Sign in / Sign up

Export Citation Format

Share Document