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.

Signal quantitative analysis using customizable perfect-translation-invariant complex wavelet functions

2014 ◽  
Vol 12 (04) ◽  
pp. 1460010 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Quantitative Analysis ◽  
Frequency Band ◽  
Wavelet Transforms ◽  
Wavelet Coefficient ◽  
Discrete Wavelet ◽  
Digital Signals ◽  
Orthonormal Wavelet ◽  
Translation Invariant ◽  
Fast Calculation ◽  
Complex Wavelet

In this paper, we introduce several methods of signal quantitative analysis using the perfect-translation-invariant complex wavelet functions (PTI complex wavelet functions), which are used in our proposed perfect-translation-invariant complex discrete wavelet transforms (PTI CDWTs) and can be designed by customization. First, using PTI complex wavelet functions, we define the continuous wavelet coefficient (CWC). Next, using orthonormal wavelet functions in the classical Hardy space, we analyze the CWC, and show that, using a CWC, we can measure the energy of a customizable frequency band, and additionally, using numbers of CWCs, we can measure the energy of the whole frequency band. Next, we introduce the fast calculation method of CWCs and show the applicability of the PTI CDWTs to digital signals. Based on them, we introduce some examples of signal quantitative analysis, including the methods to obtain instantaneous amplitude, instantaneous phase and instantaneous frequency. Additionally, we introduce the energy measurement of the whole frequency band using the PTI DT-CDWT, which is one of our proposed PTI CDWTs.

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.

scholarly journals The Improvement of Discrete Wavelet Transform

2021 ◽  
Author(s):  
Zhihua Zhang
Keyword(s):  
Wavelet Transform ◽  
Decay Rate ◽  
Discrete Wavelet Transform ◽  
Wavelet Transforms ◽  
Polynomial Interpolation ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Wavelet Coefficients ◽  
Periodic Wavelet ◽  
Improved Algorithm

Discrete wavelet transform and discrete periodic wavelet transform have been widely used in image compression and data approximation. Due to discontinuity on the boundary of original data, the decay rate of the obtained wavelet coefficients is slow. In this study, we use the combination of polynomial interpolation and one-dimensional/two-dimensional discrete periodic wavelet transforms to mitigate boundary effects. The decay rate of the obtained wavelet coefficients in our improved algorithm is faster than that of traditional two-dimensional discrete wavelet transform. Moreover, our improved algorithm can be extended naturally to the higher-dimensional case.

scholarly journals Two-Layer Fragile Watermarking Method Secured with Chaotic Map for Authentication of Digital Holy Quran

2014 ◽  
Vol 2014 ◽  
pp. 1-29 ◽  
Author(s):  
Mohammed S. Khalil ◽  
Fajri Kurniawan ◽  
Muhammad Khurram Khan ◽  
Yasser M. Alginahi
Keyword(s):  
Wavelet Transforms ◽  
Wavelet Coefficient ◽  
Chaotic Map ◽  
Spatial Domain ◽  
Fragile Watermarking ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Wavelet Domain ◽  
Good Image Quality ◽  
Holy Quran

This paper presents a novel watermarking method to facilitate the authentication and detection of the image forgery on the Quran images. Two layers of embedding scheme on wavelet and spatial domain are introduced to enhance the sensitivity of fragile watermarking and defend the attacks. Discrete wavelet transforms are applied to decompose the host image into wavelet prior to embedding the watermark in the wavelet domain. The watermarked wavelet coefficient is inverted back to spatial domain then the least significant bits is utilized to hide another watermark. A chaotic map is utilized to blur the watermark to make it secure against the local attack. The proposed method allows high watermark payloads, while preserving good image quality. Experiment results confirm that the proposed methods are fragile and have superior tampering detection even though the tampered area is very small.

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.

scholarly journals Minimizing Noise in Sinusiodal Function Signal using Wavelet Transform

2019 ◽  
Vol 9 (2) ◽  
pp. 1254-1260
Keyword(s):  
Wavelet Transforms ◽  
Wavelet Coefficient ◽  
Noise Signal ◽  
Filter Method ◽  
Fast Fourier Transformation ◽  
Original Signal ◽  
Wavelet Coefficients ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Data Signal

Resistances that occur in retrieving and processing signal is caused by the interference (noise) on the data signal measurement results. The resistance will raise uncertainties in determining the value of the frequency. This is due to the signal which is mixed with the noise in the original signal. In general, the process of signal analysis uses Fast Fourier Transformation (FFT). However, by using FFT in analyzing and reconstructing there are still doubts in determining the real frequency due to the still visible noise in the signal. In this study the signal function used is a sinusiodal function, Y = 2 sinπf1 t + 2 sin πf2 t, with a given noise value of 2 DB. The specified frequency value of f1 and f2 equal to 0.25 Hz and 5 Hz, respectively. This research proposed wavelet transforms to analyze and in filtering original signal with noise. By using the transformation wavelet, signal with noise filtered with the high pass and low pass filter method and also using the Haar wavelet function in analyzing. Once the signal is decomposed using wavelet transformation, the wavelet coefficients value will be obtained. The wavelet coefficient values will then threshold within a range of 5-50%. The purposed in determining the treshold value is to reduce the signal data identified as a noise signal data. If the value of wavelet coefficient below the treshold percentage value multiplied by the maximum wavelet coefficient, it is identified as a noise signal data, and the value of coefficient wavelet will be zero. The wavelet coefficient will then be reconstructed in order to obtain the data signal with the new sinusoidal function. In determining the value of the reconstructed frequency signal, the Fast Fourier Transform (FTT) method is used. The results of the study is signals with noise can be analyzed and filtered using wavelet transforms, by changing the signal into wavelet coefficients. Furthermore, the threshold of 5% is capable in reducing of noise in signal so that the graph of frequency and amplitude showed a clearer value of frequency.

Characteristics analysis of wavelet coefficients and its applications in image compression

2014 ◽  
Vol 12 (03) ◽  
pp. 1450028 ◽  
Author(s):  
Fangnian Lang ◽  
Jiliu Zhou ◽  
Yuan Yan Tang ◽  
Hongnian Yu ◽  
Shuang Cang ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Image Compression ◽  
Wavelet Coefficient ◽  
Correlation Property ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Wavelet Bases ◽  
Discrete Form ◽  
Still Image ◽  
Characteristics Analysis

Currently, the wavelet transform is widely used in the signal processing domain, especially in the image compression because of its excellent de-correlation property and the redundancy property included in the wavelet coefficients. This paper investigates the redundancy relationships between any two or three components of the wavelet coefficients, the wavelet bases and the original signal. We discuss those contents for every condition according to the continuous form and the discrete form, respectively, by which we also derive a uniform formula which illuminates the inherent connection among the redundancy of the wavelet coefficients, the wavelet bases and the original signals. Finally, we present the application of the wavelet coefficient redundancy property in the still image compression domain and compare the properties of the Discrete Wavelet Transform (DWT) with that of the Discrete Cosine Transform (DCT).

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.

VLSI ARCHITECTURES OF DAUBECHIES WAVELET TRANSFORMS USING ALGEBRAIC INTEGERS

2004 ◽  
Vol 13 (06) ◽  
pp. 1251-1270 ◽  
Author(s):  
KHAN WAHID ◽  
VASSIL DIMITROV ◽  
GRAHAM JULLIEN
Keyword(s):  
Power Dissipation ◽  
Wavelet Transforms ◽  
Algebraic Integer ◽  
Vlsi Architecture ◽  
Systolic Arrays ◽  
Discrete Wavelet ◽  
Daubechies Wavelet ◽  
Vlsi Architectures ◽  
Data Bus ◽  
Zero Tree

Two-Dimensional Wavelet Transforms have proven to be highly effective tools for image analysis. In this paper, we present a VLSI implementation of four- and six-coefficient Daubechies Wavelet Transforms using an algebraic integer encoding representation for the coefficients. The Daubechies filters (DAUB4 and DAUB6) provide excellent spatial and spectral locality, properties which make it useful in image compression. In our algorithm, the algebraic integer representation of the wavelet coefficients provides error-free calculations until the final reconstruction step. This also makes the VLSI architecture simple, multiplication-free and inherently parallel. Compared to other DWT algorithms found in the literature, such as embedded zero-tree, recursive or semi-recursive, linear systolic arrays and conventional fixed-point binary architectures, it has reduced hardware cost, lower power dissipation and optimized data-bus utilization. The architecture is also cascadable for computation of one- or multi-dimensional Daubechies Discrete Wavelet Transforms.

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