MATHEMATICAL IMPLEMENTATION OF HYBRID FAST FOURIER TRANSFORM AND DISCRETE WAVELET TRANSFORM FOR DEVELOPING GRAPHICAL USER INTERFACE USING VISUAL BASIC FOR SIGNAL PROCESSING APPLICATIONS

2012 ◽  
Vol 12 (05) ◽  
pp. 1240031 ◽  
Author(s):  
MOUSA K. WALI ◽  
M. MURUGAPPAN ◽  
R. BADLISHAH AHMMAD
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Input Signal ◽  
Wavelet Decomposition ◽  
Wavelet Coefficient ◽  
Visual Basic ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
End User ◽  
Decomposition Level

In recent years, the application of discrete wavelet transform (DWT) on biosignal processing has made a significant impact on developing several applications. However, the existing user-friendly software based on graphical user interfaces (GUI) does not allow the freedom of saving the wavelet coefficients in .txt or .xls format and to analyze the frequency spectrum of wavelet coefficients at any desired wavelet decomposition level. This work describes the development of mathematical models for the implementation of DWT in a GUI environment. This proposed software based on GUI is developed under the visual basic (VB) platform. As a preliminary tool, the end user can perform "j" level of decomposition on a given input signal using the three most popular wavelet functions — Daubechies, Symlet, and Coiflet over "n" order. The end user can save the output of wavelet coefficients either in .txt or .xls file format for any further investigations. In addition, the users can gain insight into the most dominating frequency component of any given wavelet decomposition level through fast Fourier transform (FFT). This feature is highly essential in signal processing applications for the in-depth analysis on input signal components. Hence, this GUI has the hybrid features of FFT with DWT to derive the frequency spectrum of any level of wavelet coefficient. The novel feature of this software becomes more evident for any signal processing application. The proposed software is tested with three physiological signal — electroencephalogram (EEG), electrocardiogram (ECG), and electromyogram (EMG) — samples. Two statistical features such as mean and energy of wavelet coefficient are used as a performance measure for validating the proposed software over conventional software. The results of proposed software is compared and analyzed with MATLAB wavelet toolbox for performance verification. As a result, the proposed software gives the same results as the conventional toolbox and allows more freedom to the end user to investigate the input signal.

DISCRETE WAVELET TRANSFORM OF FINITE SIGNALS: DETAILED STUDY OF THE ALGORITHM

2013 ◽  
Vol 12 (01) ◽  
pp. 1450001 ◽  
Author(s):  
PAVEL RAJMIC ◽  
ZDENEK PRUSA
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Detailed Analysis ◽  
Input Signal ◽  
Analysis Of Algorithms ◽  
Wavelet Coefficient ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Rigorous Analysis ◽  
Boundary Treatment

The paper presents a detailed analysis of algorithms used for the forward and the inverse discrete wavelet transform (DTWT) of finite-length signals. The paper provides answers to questions such as "how many wavelet coefficients are computed from the signal at a given depth of the decomposition" or conversely, "how many signal samples are needed to compute a single wavelet coefficient at a given depth of the decomposition" or "how many coefficients at a given depth are influenced by the selected type of boundary treatment" or "how many samples of the input signal simultaneously influence two neighboring wavelet coefficients at a given depth of the decomposition". As a byproduct, the rigorous analysis of the algorithms gives details needed for the implementation. The paper is accompanied by several Matlab functions.

ARTIFACT REMOVAL AND BRAIN RHYTHM DECOMPOSITION FOR EEG SIGNAL USING WAVELET APPROACH

2016 ◽  
Vol 78 (7-5) ◽  
Author(s):  
Syarifah Noor Syakiylla Sayed Daud ◽  
Rubita Sudirman
Keyword(s):  
Signal Processing ◽  
Wavelet Transform ◽  
Discrete Wavelet ◽  
Eeg Signal ◽  
Mother Wavelet ◽  
Decomposition Level ◽  
Biomedical Signal ◽  
Brain Rhythm ◽  
Time And Energy ◽  
Eeg Signal Processing

This recent study introduces and discusses briefly the use of wavelet approach in removing the artifacts and extraction of features for electroencephalography (EEG) signal. Many of new approaches have been discovered by the researcher for processing the EEG signal. Generally, the EEG signal processing can be divided into pre-processing and post-processing.  The aim of processing is to remove the unwanted signal and to extract important features from the signal.  However, the selections of non-suitable approach affect the actual result and wasting the time and energy.  Wavelet is among the effective approach that can be used for processing the biomedical signal.  The wavelet approach can be performed in MATLAB toolbox or by coding, that require a simple and basic command. In this paper, the application of wavelet approach for EEG signal processing is introduced. Moreover, this paper also discusses the effect of using db3 mother wavelet with 5th decomposition level of stationary wavelet transform and db4 mother wavelet with 7th decomposition level of discrete wavelet transform in removing the noise and decomposing of the brain rhythm. Besides, the simulation result are also provided for better configuration.

EEG Signals Classification Using Support Vector Machine

2020 ◽  
Vol 12 (2) ◽  
pp. 215-224
Author(s):  
Abdelhakim Ridouh ◽  
Daoud Boutana ◽  
Salah Bourennane
Keyword(s):  
Support Vector Machine ◽  
Wavelet Decomposition ◽  
Moving Average ◽  
Real Life ◽  
Support Vector ◽  
Discrete Wavelet ◽  
Eeg Signal ◽  
Eeg Signals ◽  
Decomposition Level ◽  
Sensitivity Specificity

We address with this paper some real-life healthy and epileptic EEG signals classification. Our proposed method is based on the use of the discrete wavelet transform (DWT) and Support Vector Machine (SVM). For each EEG signal, five wavelet decomposition level is applied which allow obtaining five spectral sub-bands correspond to five rhythms (Delta, Theta, Alpha, Beta and gamma). After the extraction of some features on each sub-band (energy, standard deviation, and entropy) a moving average (MA) is applied to the resulting features vectors and then used as inputs to SVM to train and test. We test the method on EEG signals during two datasets: normal and epileptics, without and with using MA to compare results. Three parameters are evaluated such as sensitivity, specificity, and accuracy to test the performances of the used methods.

Phase-based spectrum analysis method for identifying weak harmonics

2018 ◽  
Vol 24 (23) ◽  
pp. 5585-5596 ◽  
Author(s):  
Jingsong Xie ◽  
Wei Cheng ◽  
Yanyang Zi ◽  
Mingquan Zhang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Characteristic Frequency ◽  
Discrete Wavelet ◽  
Accurate Identification ◽  
Processing Methods ◽  
Characteristic Frequencies ◽  
Frequency Detection ◽  
Signal Processing Methods

Fault characteristic frequency extraction is an important means for the fault diagnosis of rotating machineries. Traditional signal processing methods commonly use the amplitude information of signals to detect damages. However, when the amplitudes of characteristic frequencies are weak, the recognition effects of traditional methods may be unsatisfactory. Therefore, this paper proposes the phase-based enhanced phase waterfall plot (EPWP) method and frequency equal ratio line (FERL) method for identifying weak harmonics. Taking a cracked rotor as an example, the characteristic frequency detection performances of the EPWP and FERL methods are compared with that of the traditional signal processing methods namely fast Fourier transform, short-time Fourier transform, discrete wavelet transform, continuous wavelet transform, ensemble empirical mode decomposition, and Hilbert–Huang transform. Research results demonstrate that the effects of EPWP and FERL for the recognitions of weak harmonics which are contained in steady signals and transient signals are better than that of the traditional signal processing methods. The accurate identification of weak characteristic frequencies in the vibration signals can provide an important reference for damage detections and improve the diagnostic accuracy.

Simultaneous Least Squares Wavelet Decomposition for Multidimensional Irregularly Spaced Data

2012 ◽  
Vol 239-240 ◽  
pp. 1213-1218 ◽  
Author(s):  
Mehdi Shahbazian ◽  
Saeed Shahbazian
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Wavelet Decomposition ◽  
Least Square ◽  
Multidimensional Case ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Wavelet Coefficients ◽  
Sampled Data ◽  
Irregularly Sampled Data

The multidimensional Discrete Wavelet Transform (DWT) has been widely used in signal and image processing for regularly sampled data. For irregularly sampled data, however, other techniques should be used including the Least Square Wavelet Decomposition (LSWD). The commonly used level by level (sequential) wavelet decomposition, which calculates the wavelet coefficients in each resolution separately, may result in a gross interpolation error. To overcome this drawback, a different approach called the Simultaneous Least Square Wavelet Decomposition, which computes all wavelet coefficients simultaneously, have been proposed by the authors. In this paper, we extend the simultaneous LSWD approach to the multidimensional case and show that this method has excellent reconstruction property for two dimensional irregularly spaced data.

Application of an Improved Wavelet Threshold Denoising Method for Vibration Signal Processing

2014 ◽  
Vol 889-890 ◽  
pp. 799-806 ◽  
Author(s):  
Zhi Jie Xie ◽  
Bao Yu Song ◽  
Yang Zhang ◽  
Feng Zhang
Keyword(s):  
Signal Processing ◽  
Wavelet Decomposition ◽  
Wavelet Coefficient ◽  
Mechanical Vibration ◽  
Vibration Signal ◽  
Threshold Function ◽  
Denoising Method ◽  
Threshold Functions ◽  
Vibration Signal Analysis ◽  
White Noises

Vibration signal analysis has been widely used in the fault detection and condition monitoring of rotation machinery. But the practical signals are easily polluted by noises in their transmission process. The raw signals should be processed to reduce noise and improve the quality before further analyzing. In this paper an improved wavelet threshold denosing method for vibration signal processing is proposed. Firstly, a new threshold is developed based on the VisuShrink threshold. The effect of noise standard deviation and wavelet coefficient is retained, and the correlation of wavelet decomposition scale is considered. Then, a new threshold function is defined. The new algorithm is able to overcome the discontinuity in hard threshold denoising method and reduce the distortion caused by permanent bias of wavelet coefficient in soft threshold denoising method. At last five kinds of threshold principles and three kinds of threshold functions are compared in processing the same signal, which is simulated as the mechanical vibration signal added white noises. The results show that the improved threshold is superior to the traditional threshold principles and the new threshold function is more effective than soft and hard threshold function in improving SNR and decreasing RMSE.

A New Approach for Optimal Decomposition Level Selection in Wavelet De-Noising

2013 ◽  
Vol 333-335 ◽  
pp. 540-545
Author(s):  
Yong Xin Zhang ◽  
Li Chen ◽  
Jian Jia ◽  
Ding Yi Fang
Keyword(s):  
White Noise ◽  
Wavelet Coefficient ◽  
Maximum Energy ◽  
Wavelet Coefficients ◽  
Decomposition Level ◽  
New Approach ◽  
Noise Test ◽  
Novel Algorithm

The paper introduces a novel algorithm to determine the optimal decomposition level in wavelet de-noising. The algorithm selects the optimal decomposition level by comparing the sparsity of wavelet coefficients at adjacent levels. The level whose wavelet coefficient has the maximum sparsity can be confirmed as the optimal decomposition level. We demonstrate experimentally that wavelet de-noising performs better using optimal decomposition level determined by our proposed algorithm than White Noise Test (WNT) method and Maximum Energy (ME) method.

Wavelet‐transform‐based prestack multiscale Kirchhoff migration

Geophysics ◽  
2004 ◽  
Vol 69 (6) ◽  
pp. 1505-1512 ◽  
Author(s):  
Zhou Yu ◽  
George A. McMechan ◽  
Phil D. Anno ◽  
John F. Ferguson
Keyword(s):  
Wavelet Transform ◽  
Wavelet Decomposition ◽  
Computational Cost ◽  
Synthetic Data ◽  
Phase Distortion ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Kirchhoff Migration ◽  
Individual Scale ◽  
The Individual

We propose a Kirchhoff‐style algorithm that migrates coefficients obtained by wavelet decomposition of seismic traces over time. Wavelet‐based prestack multiscale Kirchhoff migration involves four steps: wavelet decomposition of the seismic data, thresholding of the resulting wavelet coefficients, multiscale Kirchhoff migration, and image reconstruction from the multiscale images. The migration procedure applied to each wavelet scale is the same as conventional Kirchhoff migration but operates on wavelet coefficients. Since only the wavelet coefficients are migrated, the cost of wavelet‐based migration is reduced compared to that of conventional Kirchhoff migration. Kirchhoff migration of wavelet‐decomposed data, followed by wavelet reconstruction, is kinematically equivalent to and yields similar migrated signal shapes and amplitudes as conventional Kirchhoff migration when data at all wavelet scales are included. The decimation in the conventional discrete pyramid wavelet decomposition introduces a translation‐variant phase distortion in the wavelet domain. This phase distortion is overcome by using a stationary wavelet‐transform rather than the conventional discrete wavelet‐transform of the data to be migrated. A wavelet reconstruction operator produces a single composite broadband migrated space‐domain image from multiscale images. Multiscale images correspond to responses in different frequency windows, and migrating the data at each scale has a different cost. Migrating some, or only one, of the individual scale data sets considerably reduces the computational cost of the migration. Successful 2D tests are shown for migrations of synthetic data for a point‐diffractor model, a multilayer model, and the Marmousi model.

The Morlet and Daubechies Wavelet Transforms for Fatigue Strain Signal Analysis

2013 ◽  
Vol 471 ◽  
pp. 197-202 ◽  
Author(s):  
T.E. Putra ◽  
S. Abdullah ◽  
Mohd Zaki Nuawi ◽  
Mohd Faridz Mod Yunoh
Keyword(s):  
Wavelet Transforms ◽  
Signal Analysis ◽  
Wavelet Coefficient ◽  
Discrete Wavelet ◽  
Daubechies Wavelet ◽  
Wavelet Coefficients ◽  
Public Road ◽  
Road Surfaces ◽  
Strain Signal ◽  
Wavelet Family

This paper presents the convenient wavelet family for the fatigue strain signal analysis based on the wavelet coefficients. This study involves the Morlet and Daubechies wavelet coefficients using both the Continuous and Discrete Wavelet Transforms, respectively. The signals were collected from a front lower suspension arm of a passenger car by placing strain gauges at the highest stress locations. The car was driven over public road surfaces, i. e. pavé, highway and UKM roads. In conclusion, the Daubechies wavelet was the convenient wavelet family for the analysis. It was because the wavelet gave the higher wavelet coefficient values indicating that the resemblance between the wavelet and the signals was stronger, closer and more similar.

scholarly journals Optimal Estimation of Wavelet Decomposition Level for a Matching Pursuit Algorithm

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 843 ◽  
Author(s):  
Dmitry Kaplun ◽  
Alexander Voznesenskiy ◽  
Sergei Romanov ◽  
Erivelton Nepomuceno ◽  
Denis Butusov
Keyword(s):  
Spectral Analysis ◽  
Wavelet Decomposition ◽  
Matching Pursuit ◽  
Approximation Error ◽  
Discrete Wavelet ◽  
Processing Unit ◽  
Central Processor ◽  
Minimum Entropy ◽  
Decomposition Level ◽  
Matching Pursuit Algorithm

In this paper, we consider the application of the matching pursuit algorithm (MPA) for spectral analysis of non-stationary signals. First, we estimate the approximation error and the performance time for various MPA modifications and parameters using central processor unit and graphics processing unit (GPU) to identify possible ways to improve the algorithm. Next, we propose the modifications of discrete wavelet transform (DWT) and package wavelet decomposition (PWD) for further use in MPA. We explicitly show that the optimal decomposition level, defined as a level with minimum entropy, in DWT and PWD provides the minimum approximation error and the smallest execution time when applied in MPA as a rough estimate in the case of using wavelets as basis functions (atoms). We provide an example of entropy-based estimation for optimal decomposition level in spectral analysis of seismic signals. The proposed modification of the algorithm significantly reduces its computational costs. Results of spectral analysis obtained with MPA can be used for various signal processing applications, including denoising, clustering, classification, and parameter estimation.

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