The wavelet transform, time-frequency localization and signal analysis

1990 ◽  
Vol 36 (5) ◽  
pp. 961-1005 ◽  
Author(s):  
I. Daubechies
Keyword(s):  
Wavelet Transform ◽  
Signal Analysis ◽  
Time Frequency ◽  
Time Frequency Localization

CWT × DWT × DTWT × SDTWT: Clarifying terminologies and roles of different types of wavelet transforms

2020 ◽  
Vol 18 (06) ◽  
pp. 2030001 ◽  
Author(s):  
Rodrigo Capobianco Guido ◽  
Fernando Pedroso ◽  
André Furlan ◽  
Rodrigo Colnago Contreras ◽  
Luiz Gustavo Caobianco ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Discrete Time ◽  
Wavelet Transforms ◽  
Signal Analysis ◽  
Applied Mathematics ◽  
Discrete Wavelet ◽  
Frequency Signal ◽  
Time Frequency ◽  
Subsequent Investigation ◽  
Different Types

Wavelets have been placed at the forefront of scientific researches involving signal processing, applied mathematics, pattern recognition and related fields. Nevertheless, as we have observed, students and young researchers still make mistakes when referring to one of the most relevant tools for time–frequency signal analysis. Thus, this correspondence clarifies the terminologies and specific roles of four types of wavelet transforms: the continuous wavelet transform (CWT), the discrete wavelet transform (DWT), the discrete-time wavelet transform (DTWT) and the stationary discrete-time wavelet transform (SDTWT). We believe that, after reading this correspondence, readers will be able to correctly refer to, and identify, the most appropriate type of wavelet transform for a certain application, selecting relevant and accurate material for subsequent investigation.

Research and Implementation of Image Fusion Algorithm Based on Wavelet Transform

2011 ◽  
Vol 187 ◽  
pp. 683-687
Author(s):  
Kuang Ling
Keyword(s):  
Wavelet Transform ◽  
Image Fusion ◽  
Research Focus ◽  
Fusion Algorithm ◽  
Simulation Experiments ◽  
Time Frequency ◽  
Directional Characteristics ◽  
Time Frequency Localization ◽  
Analysis Of Performance ◽  
Important Branch

Image fusion is the important branch and research focus of intelligence fusion and it has been well applied in many areas such as military, remote sensing, robotics as well as intelligent transportation. This paper applies the time-frequency localization as well as directional characteristics of wavelet transform and conducts sub-tree partition on the decomposed high-frequency coefficient to improve the contrast gradient of the image, regarding the sub-tree as a unit. This method is achieved under the VC environment. Finally, the analysis of performance indicators such as simulation experiments, entropy and average gradient shows that the algorithm can effectively reduce the distortion of blending image and it is an effective image fusion algorithm.

Application of Wavelet Analysis in the DPIV Information Processing for the River Model Test

2011 ◽  
Vol 287-290 ◽  
pp. 2797-2800
Author(s):  
Dong Zi Pan ◽  
Ying Li ◽  
Gang Chen
Keyword(s):  
Wavelet Transform ◽  
Model Test ◽  
High Speed ◽  
Fluid Flows ◽  
Horizontal Distribution ◽  
Model Verification ◽  
Image Feature ◽  
Time Frequency ◽  
Time Frequency Localization ◽  
Scheme Selection

It’s important to measure the horizontal distribution of the 2D velocity field for model verification and scheme selection at model test in the tidal estuary. Digital particle image velocimetry (DPIV) has become an accepted technique for the measurement of two- and three component planar velocities in a wide variety of fluid flows, which has advantages of high speed and nil interference. However, sometimes DPIV images are overexposure, uneven distribution of the gray values, and obscurity on the edges of the particles, which will affect the accuracy of flow data by inversion. Wavelet transform has good characteristics in time-frequency localization, and it has been widely used for image preprocessing, image compression, image restoration, image feature extraction and pattern recognition. A wavelet-based multi-resolution technique was applied to analyze the 2D measurement results of a DPIV system in this paper. In the different stages: boundary treatment, noise reduction, identification and elimination of the error vector, which are applicable to the processing of the DPIV information for getting the velocity vectors with higher resolution and precision through the continuous wavelet transform of velocity data.

scholarly journals Research on EMI Noise Measurement Technology Based on Wavelet Analysis

2018 ◽  
Vol 2 (1) ◽  
Author(s):  
Xu Li
Keyword(s):  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Electromagnetic Interference ◽  
Open Space ◽  
Threshold Function ◽  
Measurement Technology ◽  
Noisy Environment ◽  
Time Frequency ◽  
Filtering Method ◽  
Time Frequency Localization

Aiming at the problem that it is difficult to measure the electromagnetic radiation produced by the equipment at present, this paper presents a method for measuring the noise of electromagnetic interference (EMI) based on wavelet analysis. The technique uses time frequency localization features of the wavelet transform, based on threshold function filtering method to filter the test signal, which makes it possible in open space or noisy environment for measurement of electromagnetic interference  of  equipment. Simulation  and experimental results show that the technique is able to eliminate or attenuate the noise in the frequency band of 30Hz~1000MHz.

Application of Harmonic Wavelet Analysis to Rubbing Vibration Signals for Rotating Machinery Fault Diagnosis

2013 ◽  
Vol 321-324 ◽  
pp. 1245-1248
Author(s):  
Xiang Wang ◽  
Yuan Zheng
Keyword(s):  
Wavelet Transform ◽  
Signal Analysis ◽  
Rotating Machinery ◽  
The Other ◽  
Vibration Signals ◽  
Time Frequency ◽  
Vibration Data ◽  
Turbo Generator ◽  
Harmonic Wavelet ◽  
Machinery Fault Diagnosis

Harmonic wavelet transform (HWT)and harmonic wavelet time-frequency profile plot (TFPP) is introduced firstly in practice to identify weak singularity in a signal with noise clearly. With TFPP method, emulational signal and vibration data of the rubbing of the large practical turbo-generator units are analyzed successfully, which prove that the method is effectively extract the rubbing signal feature which is can not gained by the other signal analysis methods, and the rubbing of the turbo-generator units is identified effectively.

scholarly journals Non-decimated Wavelet Transform for a Shift-invariant Analysis

2018 ◽  
Vol 19 (1) ◽  
pp. 93 ◽  
Author(s):  
Gabriela De Oliveira Nascimento Brassarote ◽  
Eniuce Menezes de Souza ◽  
João Francisco Galera Monico
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Signal Analysis ◽  
Perfect Reconstruction ◽  
Discrete Wavelet ◽  
Continuous Version ◽  
Time Frequency ◽  
Application Potential ◽  
Invariant Analysis ◽  
Analysis Of Time Series

Due to the ability of time-frequency location, the wavelet transform hasbeen applied in several areas of research involving signal analysis and processing,often replacing the conventional Fourier transform. The discrete wavelet transformhas great application potential, being an important tool in signal compression,signal and image processing, smoothing and denoising data. It also presentsadvantages over the continuous version because of its easy implementation, goodcomputational performance and perfect reconstruction of the signal upon inversion.Nevertheless, the downsampling required in the discrete wavelet transformcalculous makes it shift variant and not appropriated to some applications, suchas for signals or time series analysis. On the other hand, the Non-Decimated DiscreteWavelet Transform is shift-invariant because it eliminates the downsamplingand, consequently, is more appropriate for identifying both stationary and nonstationarybehaviors in signals. However, the non-decimated wavelet transform hasbeen underused in the literature. This paper intends to show the advantages ofusing the non-decimated wavelet transform in signal analysis. The main theoricaland pratical aspects of the multiscale analysis of time series from non-decimatedwavelets in terms of its formulation using the same pyramidal algorithm of thedecimated wavelet transform was presented. Finally, applications with a simulatedand real time series compare the performance of the decimated and non-decimatedwavelet transform, demonstrating the superiority of non-decimated one, mainly dueto the shift-invariant analysis, patterns detection and more perfect reconstructionof a signal.

Transient Power Quality Disturbances Identification and Classification Using Wavelet and Support Vector Machines

2012 ◽  
Vol 433-440 ◽  
pp. 1071-1077
Author(s):  
Wen Sheng Sun ◽  
Xiang Ning Xiao ◽  
Shun Tao ◽  
Jian Wang
Keyword(s):  
Wavelet Transform ◽  
Support Vector Machines ◽  
Power Quality ◽  
Support Vector ◽  
Time Frequency ◽  
Vector Machines ◽  
Power Quality Disturbance ◽  
Time Frequency Localization ◽  
Power Quality Disturbances ◽  
Transient Power Quality

Based on wavelet transform and support vector machines, a method of recognition and classification of transient power quality disturbance is presented. Using wavelet transform time-frequency localization characteristics, according to the principle of modulus maxima, realize the automatic detection positioning. After multi-resolution signal decomposition of PQ disturbances, multi-scale information in frequency domain and time domain of the signal can be extracted as the characteristic vectors. After choose and optimization of the eigenvectors based on the method of F-score, support vector machines are used to classify these eigenvectors of power quality disturbances. Effectiveness of the proposed method is verified through Matlab simulation.

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