Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

Thermal Decomposition Mechanism and Non Isothermal Kinetics of Complex of [La_2(P-MBA)_6(PHEN)_2]2H_2O

The complex of [La 2(P MBA) 6(PHEN) 2]2H 2O (P MBA: p methylbenzoate and PHEN: 1,10 phenanthroline) was prepared and characterized by elemental analysis and IR spectroscopy. The thermal behavior of [La 2(P MBA) 6(PHEN) 2]2H 2O in dynamic nitrogen atmosphere was investigated by TG DTG techniques. The results show that the thermal decomposition process of the [La 2(P MBA) 6(PHEN) 2]2H 2O occurs in five steps. The empirical kinetic model for the first step thermal decomposition obtained by Malek method is SB(m,n). The activation energy E and the pre exponential factor lnA for this step reaction are 76.4 kJ·mol -1 and 24.92, respectively.

Study on Non-Isothermal Decomposition Kinetics of Ephedrini Hydrochloridum

The thermal decomposition processes of ephedrini hydrochloridum and its kinetics are studied by TG-DTG techniques. A combined method, which includes Achar method, Coats-Redfera method, and Ozawa method, is put forward for determining kinetic model under non-isothermal conditions. By applying the combined method, it is determined that the thermal decomposition of ephedrini hydrochloridum is subjected to cylindrical symmetric diffusion. And the reaction function isƒ(α)=2(1-α)?, apparent activation energy (115.26±3.55) kJ·mol−1, pre-exponential factor 4.62×108 s−1. Results show that the combined method is feasible and simple.

Studies on Non-isothermal Kinetics of Thermal Decomposition of Strontium Chloride Hexahydrate

The thermal decomposition of the strontium chloride hexahydrate and its kinetics were studied under non isothermal condition in nitrogen by thermogravimetric and derivative thermogravimetric techniques. The intermediate and residue for each decomposition were identified from TG curve. The non isothermal kinetic data were analyzed by the Achar method and the Coats Redfern method. The possible reaction mechanisms were suggested by comparing the kinetic parameters. The kinetic equation for the first stage can be expressed as d α /d t = A exp(- E/RT)(1-α ), the second stage, d α /d t = A exp(- E/RT)3(1-α ) 2/3 , and the third stage, d α /d t = A exp(- E/RT)3/2(1-α ) 2/3 [1-(1- α ) 1/3 ] -1 . Mathematic expressions of the kinetic compensation effects of each stage of the thermal decomposition reaction were also obtained.

Non-isothermal Decomposition Mechanism and Kinetics of LiClO_4 in Nitrogen

The non-isothermal decomposition kinetics of LiClO4 in flow N2 atmosphere was studied. TG-DTA curves show that the decomposition proceeded through two well-defined steps below 900℃, and the mass loss was in agreement with the theoretical value. XRD profile demonstrates that the product of the thermal decomposition at 500℃ is LiCI. For the decomposition kinetics study, the activation energies calculated with the Friedman method were considered as the initial values for non-linear regression and were used for verifying the correctness of the fired models. The decomposition process was fitted by a two-step consecutive reaction： extended Prout-Tompkins equation[Bna, f（α） is （1-α）^nα^α] followed by a lth order reaction（F1）. The activation energies were （215.6±0.2） and （251.6±3.6） kJ/mol, respectively. The exponentials n and a for Bna reaction were （0.25±0.05） and （0.795±0.005）, respectively. The reaction types and activation energies were in agreement with those obtained from the isothermal method, but the exponentials were optimized for better firing and prediction.

Kinetics Study on the Thermal Decomposition of Europium p-methyl-benzoate Complex with 1,10-penanthroline under Non-isothermal Con-ditions

The thermal decomposition reaction of Eu-2(p-MBA)(6)(PHEN)(2) (p-MBA=CH3C6H4COO, methylbenzoate; PHEN=C12H8N2, 1,10-phenanthroline) was studied in a static atmosphere using TG-DTG method. The thermal decomposition process of the complex was determined and its kinetics was investigated. Kinetic parameters were obtained from the analysis of TG-DTG curves by means of the Achar method and the Madhusudanan-Krishnan-Ninan (MKN) method. The most probable mechanism functions of the thermal decomposition reaction for the first stage are: f(alpha) =(1-alpha)(2), g(alpha) = (1-alpha)(-1)-1. The activation energy for the first stage is 255.18 kJ/mol, the entropy of activation DeltaS is 227.32 J/mol and the Gibbs free energy of activation DeltaG is 128.04 W/mol.

Influences of reaction conditions on methane decomposition over non-supported Ni catalyst

Effects of reaction temperature and methane gas hourly space velocity （GHSV） on methane decomposition over non-supported Ni catalyst have been investigated in this work.Methane molecules activation,Ni particles growth and nano-carbon diffusion were the main factors influencing methane decomposition stability of non-supported Ni.The results of methane decomposition activity test on the non-supported Ni catalyst showed that the prepared non-supported Ni could exhibit a good methane decomposition performance with 273 gC/gNi and 2667 molH2/molNi at 500 -C and 45000 mL/（gcat h）.Scanning electron microscope （SEM）,X-ray powder diffraction （XRD） and temperature-programmed oxi- dation （TPO） have been carried out to characterize the used catalysts.The deposited carbon was carbon nanofibers,among which graphitic carbon formation increased with the reaction time of methane decomposition.Ni particle size was not the decisive factor during the carbon growing stage.

Recursive State-space Model Identification of Non-uniformly Sampled Systems Using Singular Value Decomposition

In this paper a recursive state-space model identification method is proposed for non-uniformly sampled systems in industrial applications. Two cases for measuring all states and only output(s) of such a system are considered for identification. In the case of state measurement, an identification algorithm based on the singular value decomposition(SVD) is developed to estimate the model parameter matrices by using the least-squares fitting. In the case of output measurement only, another identification algorithm is given by combining the SVD approach with a hierarchical identification strategy. An example is used to demonstrate the effectiveness of the proposed identification method.

Non-phosgene synthesis of hexamethylene-1,6-diisocyanate from thermal decomposition of hexamethylene-1,6-dicarbamate over Zn–Co bimetallic supported ZSM-5 catalyst

A non-phosgene route for the synthesis of hexamethylene-1,6-diisocyanate(HDI) was developed via catalytic decomposition of hexamethylene-1,6-dicarbamate(HDC) over Zn–Co bi-metallic supported ZSM-5 catalyst.The catalyst was characterized by FTIR and XRD analyses. Three solvents dioctyl sebacate(DOS), dibutyl sebacate(DBS) and 1-butyl-3-methylimidazolium tetrafluoroborate(BMIMBF_4) were investigated and compared; DOS gave better performance. The catalytic performances for thermal decomposition of HDC to HDI using DOS as solvent were then investigated, and the results showed that, under the optimized reaction conditions, i.e.,10 wt%concentration of HDC in DOS, 250 °C temperature, 60 min reaction time, 83.8% yield of HDI had been achieved over Zn–Co/ZSM-5. Decomposition of the intermediate hexamethylene-1-carbamate-6-isocyanate(HMI) over Zn–Co/ZSM-5 in DOS solvent was further studied and the results indicated that yield of HDI from HMI reached to 69.6%(98.6% HDI selectively) at 270 °C, which further increased the yield of the total HDI(HDI_(tol)) to as high as 95.0%. Recycling of catalyst showed that HDI and HMI yield slightly decreased, and by-product yield increased after the catalyst was reused for 4 times. At last possible reaction mechanism was proposed.

Derivative of a Determinant with Respect to an Eigenvalue in the <i>LDU</i>Decomposition of a Non-Symmetric Matrix

We demonstrate that, when computing the LDU decomposition (a typical example of a direct solution method), it is possible to obtain the derivative of a determinant with respect to an eigenvalue of a non-symmetric matrix. Our proposed method augments an LDU decomposition program with an additional routine to obtain a program for easily evaluating the derivative of a determinant with respect to an eigenvalue. The proposed method follows simply from the process of solving simultaneous linear equations and is particularly effective for band matrices, for which memory requirements are significantly reduced compared to those for dense matrices. We discuss the theory underlying our proposed method and present detailed algorithms for implementing it.

Thermal decomposition mechanism and non-isothermal kinetics of the polyoxometalate of ciprofloxacin with 12-tungstoboric acid

The polyoxometalate complex (CPFX-HCl)(4)H5BW12O40-12H(2)O was prepared in aqueous solution for the first time, and characterized by elemental analysis, IR spectrum, and TG-DTG. The TG-DTG curves showed that its thermal decomposition was a four-step process consisting of the simultaneous collapse of Keggin anion. The intermediate and residue of the decomposition were identified by mean of TG-DTG, IR, and XRD technique. The non-isothermal kinetic data were analyzed by the Achar method and Coats-Redfern method. The apparent activation energy (E) and the pre-exponential factor (In A) of each decomposition were obtained. The most probable thermal decomposition reaction mechanisms were proposed by comparison of the kinetic parameters. The kinetic equation for both the second stage and the third stage can be expressed as d alpha/dt = Ae(-E/RT) -(1 - alpha)(2), and the fourth stage d alpha/dt = Ae(-E/RT) -(1 - alpha). And their mathematic expressions of the kinetic compensation effects of thermal decomposition reaction were also determined.

Double Elzaki Transform Decomposition Method for Solving Non-Linear Partial Differential Equations

In this paper, we discuss a new method employed to tackle non-linear partial differential equations, namely Double Elzaki Transform Decomposition Method (DETDM). This method is a combination of the Double ELzaki Transform and Adomian Decomposition Method. This technique is hereafter provided and supported with necessary illustrations, together with some attached examples. The results reveal that the new method is very efficient, simple and can be applied to other non-linear problems.

NON-DESTRUCTIVE PAVEMENT LAYER THICKNESS MEASUREMENT USING EMPIRICAL MODE DECOMPOSITION WITH GPR

Ground Penetrating Radar(GPR) is an effective Non-Destructive Testing(NDT) technique for highway pavement surveys, which is able to acquire continuous pavement data compared with traditional core drilling method. In this study, we proposed an accurate and efficient method to estimate the thickness of each pavement layer using an air-coupled GPR system. For this work, the main difficulties are estimating each pavement layer's time delay and dielectric constant. We first give the basic signal model for pavement evaluation, and then present an Intrinsic Mode Functions(IMFs) product detector to determine each pavement layer's time delay. This method is based on Empirical Mode Decomposition(EMD), which is an adaptive signal decomposition procedure and proved to be suitable for suppressing noises in GPR signal. The dielectric constant was determined by metal reflection measurement. The laboratory and highway experiments illustrate that the proposed thickness estimation method yields reasonable result, thus meets the requirements of practical highway pavement survey with massive GPR data.

Thermal Decomposition Behavior and Kinetic Study of Jamadoba Coal and Its Density Separated Macerals: A Non-Isothermal Approach

This kinetic study focuses on determining the thermal gravimetric profile of a particular grade of Indian sub-bituminous coal. A thermogravimetric analyzer (TGA-1000) was employed to investigate the thermal behavior and extract the kinetic parameters of Jamadoba coal and its corresponding density separated macerals. The weight loss was measured in air atmosphere. The coal samples used in this study were obtained from Jamadoba mines, Jharkhand. Samples of 35 mg and 200 μm mean size were subjected to synthetic air atmospheres (21% O2). Heating rates of 2, 5 and 7°C/min were applied until the temperature reached 1400°C, which was kept constant until burnout. Low heating rate was preferred so that devolatilization occurs prior to ignition and combustion. Derivative thermogravimetry (DTG) analysis method was applied to measure the weight changes and rates of weight loss used for calculating the kinetic parameters. The activation energy (Ea) and pre-exponential factor were obtained from model-free methods by applying non-isothermal thermogravimetry analysis.

Characterization and Non-isothermal Decomposition Kinetic Analysis of PS/FeNi_3 Nanocomposites

Polystyrene/iron-nickel （PS/FeNi3） nanocomposites were synthesized via an in-situ polymerization route and characterized by XRD,SEM and FTIR. FeNi3 nanoparticles were characterized by TEM and XRD. The pure FeNi3 nanoparticles （100～125 nm） were highly clustered and percolated through the PS matrix. When the content of FeNi3 nanoparticles reached 5 wt%,an interaction between FeNi3 nanoparticles and PS matrix was observed. The thermal decomposition behavior of PS/FeNi3 nanocomposites was investigated by thermal analysis. The activation energies （E） and pre-exponential factors （lnA） were calculated by using Archar method. The results show that the thermal decomposition of pure PS is a one-dimensional diffusion mechanism. A three-dimensional diffusion mechanism appears when FeNi3 nanoparticles incorporate. The E of PS/FeNi3 nanocomposites with different FeNi3 contents is 217.5,225.3,180.6 and 73.0 kJ·mol-1,and the corresponding lnA is 35.6,34.9,27.5 and 10.4 S-1,respectively.

Decomposition mechanisms and non-isothermal kinetics of LiHC_2O_4·H_2O

The thermal decomposition process of LiHC2O4·H2O from 30 to 600 ℃ was investigated by the thermogravimetric and differential scanning calorimetry (TG-DSC). The phases decomposited at different temperature were characterized by X-ray diffraction (XRD), which indicated the decompositions at 150, 170, and 420℃, relating to LiHC2O4, Li2C2O4, Li2C2O4, and Li2CO3, respectively. Reaction mechanisms in the whole sintering process were determined, and the model fitting kinetic approaches were applied to data for non-isothermal thermal decomposition of LiHC2O4?H2O; finally, the kinetic parameters of each reaction were also calculated herein.

A novel trilinear decomposition algorithm:Three-dimension non-negative matrix factorization

Non-negative matrix factorization （NMF） is a technique for dimensionality reduction by placing non-negativity constraints on the matrix. Based on the PARAFAC model, NMF was extended for three-dimension data decomposition. The three-dimension nonnegative matrix factorization （NMF3） algorithm, which was concise and easy to implement, was given in this paper. The NMF3 algorithm implementation was based on elements but not on vectors. It could decompose a data array directly without unfolding, which was not similar to that the traditional algorithms do, It has been applied to the simulated data array decomposition and obtained reasonable results. It showed that NMF3 could be introduced for curve resolution in chemometrics.

Synthesis, Characterization, Thermal Decomposition Mechanism and Non-Isothermal Kinetics of Salicylaldehyde Salicylhydrazone and Its Complex of Erbium(Ⅲ)

The salicylaldehyde salicylhydrazone and its complex of Er(Ⅲ) were synthesized. The formulae K·4H_2O(HL=[C_(14)H_(10)N_2O_3]^(2-), the bivalent form of the salicylaldehyde salicylhydrazone) were determined by elemental analysis and EDTA volumetric analysis. Molar conductance, IR, UV and X-ray power diffraction were carried out for the characterizations of the complex and the ligand. There are two stable five-numbered and six-numbered circles in the complex. The thermal decompositions of the ligand and the complex with the kinetic study are carried out by non-isothermal thermogravimetry. The stages of the decompositions were identified by TG-DTG curve. The non-isothermal kinetic data were analyzed by means of integral and differential methods. The possible reaction mechanism and the kinetic equation were investigated by the corresponding kinetic parameters.The activation energy value of the main step decomposition are also calculated by Kissinger′s method and Ozawa′s method.

Non-isothermal Decomposition Kinetics of K(AHDNE)

The thermal behavior and non-isothermal decomposition kinetics of 1-amino-1-hydrazino-2,2-dinitro-ethylene potassium salt[K（AHDNE）] were studied under the non-isothermal conditions by different scanning calorimeter（DSC） method. The thermal behavior of K（AHDNE） presents three exothermic decomposition processes. The kinetic equation of the first thermal decomposition reaction obtained is dα/dT=（1019.63/β）3（1-α）[-ln（1-α）]2/3exp（-1.862× 105/RT）. The self-accelerating decomposition temperature（TSADT） and critical temperature of thermal explosion（Tb） of K（AHDNE） are 162.5 and 171.4 °C, respectively. K（AHDNE） has higher thermal stability than AHDNE.