AAK Theorem and a Design of Multidimensional BIBO Stable Filters

Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.

Characterization of functionalized multiwalled carbon nanotubes and application as an effective filter for heavy metal removal from aqueous solutions

Filtration efficiency of Ni(II) from aqueous solution using pristine and modified MWCNTs filters was investigated as a function of Ni(II) ion concentration, p H, and filter mass. MWCNTs were synthesized by CVD method and modified using two complementary treatments, purification(using a mixture of hydrochloric acid and hydrogen peroxide) and functionalization(using nitric acid). The effect and mechanism of each treatment on the structural integrity of pristine MWCNTs has been studied. Morphology of the pristine and modified filters was investigated by Raman Spectrometry(RS), Scanning Electron Microscopy(SEM), Energy Dispersive X-ray Spectroscopy(EDS),Fourier Transform Infrared(FTIR) spectrometry and Thermogravimetric analysis. It was found from Raman spectra that the ratio of the intensity of D-band to that of G-band decreased by purification process, and increased by functionalization process. The adsorption mechanism of Ni(II) onto the surface functional groups of modified MWCNTs was confirmed by FTIR spectrum. The filtration results showed that the removal efficiency of Ni(II) is strongly dependent on pH and could reach 85% at pH = 8. Also, modified MWCNT filters can be reused through many cycles of regeneration with high performance. Functionalized MWCNTs filters may be a promising adsorbent candidate for heavy metal removal from wastewater.

A Multivariate Empirical Orthogonal Function-Based Scheme for the Balanced Initial Ensemble Generation of an Ensemble Kalman Filter

The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful choice of an initial ensemble perturbation method that dynamically cycles ensemble perturbations is required for the optimal performance of the system. Based on the multivariate empirical orthogonal function (MEOF) method, a new ensemble initialization scheme is developed to generate balanced initial perturbations for the ensemble Kalman filter (EnKF) data assimilation, with a reasonable consideration of the physical relationships between different model variables. The scheme is applied in assimilation experiments with a global spectral atmospheric model and with real observations. The proposed perturbation method is compared to the commonly used method of spatially-correlated random perturbations. The comparisons show that the model uncertainties prior to the first analysis time, which are forecasted from the balanced ensemble initial fields, maintain a much more reasonable spread and a more accurate forecast error covariance than those from the randomly perturbed initial fields. The analysis results are further improved by the balanced ensemble initialization scheme due to more accurate background information. Also, a 20-day continuous assimilation experiment shows that the ensemble spreads for each model variable are still retained in reasonable ranges without considering additional perturbations or inflations during the assimilation cycles, while the ensemble spreads from the randomly perturbed initialization scheme decrease and collapse rapidly.

Development and Experiment of Multi- functional Wood Dehumidification Dryer

A multi functional wood dehumidification dryer has been developed recently. The dryer can carry out air dehumidification by using only one refrigeration system, in which heat supplying and moisture air are exhausted by changing the position of several air dampers. In this paper, the work principles and characteristics of the dehumidification dryer are introduced, and the testing results about the thermal engineering performance of the dehumidification dryer, as well as the experiment results of drying several species of lumbers are expounded.

Particle filter with importance density function generated by updated system equation

The current measurement was exploited in a more efficient way. Firstly, the system equation was updated by introducing a correction term, which depends on the current measurement and can be obtained by running a suboptimal filter. Then, a new importance density function(IDF) was defined by the updated system equation. Particles drawn from the new IDF are more likely to be in the significant region of state space and the estimation accuracy can be improved. By using different suboptimal filter, different particle filters(PFs) can be developed in this framework. Extensions of this idea were also proposed by iteratively updating the system equation using particle filter itself, resulting in the iterated particle filter. Simulation results demonstrate the effectiveness of the proposed IDF.

Nonlinear Measurement Function in the Ensemble Kalman Filter

ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions： the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.

A Fusion Kalman Filter and UFIR Estimator Using the Influence Function Method

In this paper,the Kalman filter(KF)and the unbiased finite impulse response(UFIR)filter are fused in the discrete-time state-space to improve robustness against uncertainties.To avoid the problem where fusion filters may give up some advantages of UFIR filters by fusing based on noise statistics,we attempt to find a way to fuse without using noise statistics.The fusion filtering algorithm is derived using the influence function that provides a quantified measure for disturbances on the resulting filtering outputs and is termed as an influence finite impulse response(IFIR)filter.The main advantage of the proposed method is that the noise statistics of process noise and measurement noise are no longer required in the fusion process,showing that a critical feature of the UFIR filter is inherited.One numerical example and a practice-oriented case are given to illustrate the effectiveness of the proposed method.It is shown that the IFIR filter has adaptive performance and can automatically switch from the Kalman estimate to the UFIR estimates according to operating conditions.Moreover,the proposed method can reduce the effects of optimal horizon length on the UFIR estimate and can give the state estimates of best accuracy among all the compared methods.

UNIFORM ANALYTIC CONSTRUCTION OF WAVELET ANALYSIS FILTERS BASED ON SINE AND COSINE TRIGONOMETRIC FUNCTIONS

Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.

Correlation Degree and Correlation Coefficient of Multi-Output Functions

We present definitions of the correlation degree and correlation coefficient of multi-output functions. Two relationships about the correlation degree of multi-output functions are proved. One is between the correlation degree and independency, the other is between the correlation degree and balance. Especially the paper discusses the correlation degree of affine multioutput functions. We demonstrate properties of the correlation coefficient of multi-output functions. One is the value range of the correlation coefficient, one is the relationship between the correlation coefficient and independency, and another is the sufficient and necessary condition that two multi-output functions are equivalent to each other.

Filtering Function Method for the Cauchy Problem of a Semi-Linear Elliptic Equation

A Cauchy problem for the semi-linear elliptic equation is investigated. We use a filtering function method to define a regularization solution for this ill-posed problem. The existence, uniqueness and stability of the regularization solution are proven;a convergence estimate of H?lder type for the regularization method is obtained under the a-priori bound assumption for the exact solution. An iterative scheme is proposed to calculate the regularization solution;some numerical results show that this method works well.

S-type Er-Yb Co-doped Phosphate Glass Waveguide Amplifier Integrated with Cascaded Multilayer Medium Thin Film Filter

A new S-type of erbium-ytterbium co-doped phosphate glass waveguide amplifier integrated with cascaded multilayer medium thin film filter is proposed,this S-type geometry waveguide structure is used to achieve a long path in a compact chip,and obtained higher gain with lower Er-doped concentration. The cascaded multilayer medium thin film filter is utilized to achieve a broader flattening gain bandwidth.The intrinsical gain spectrum is obtained by solving rate and power propagation equations,the effect of transmittance spectrum of thin film filter on flattening gain is discussed.

Delay-dependent Non-fragile H_∞ Filtering for Uncertain Fuzzy Systems Based on Switching Fuzzy Model and Piecewise Lyapunov Function

This paper is concerned with the non-fragile H∞ filter design problem for uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with time delay. To begin with, the T-S fuzzy system is transformed to an equivalent switching fuzzy system. Then, based on the piecewise Lyapunov function and matrix decoupling technique, a new delay-dependent non-fragile H∞ filtering method is proposed for the switching fuzzy system. The proposed condition is less conservative than the previous results. Since only a set of LMIs is involved, the filter parameters can be solved directly. Finally, a design example is provided to illustrate the validity of the proposed method.

Receiver Function Estimated by Wiener Filtering

Wiener filtering is used to estimate receiver function in a time_domain. With the vertical component of 3_component teleseismic P waveform as the input of a Wiener filter, receiver function as the filter response, and radial and tangential components as the expected output, receiver function is estimated by minimizing the error between expected and actual outputs. Receiver function can be obtained by solving the Toeplitz equation using the Levinson algorithm. The non_singularity of the Toeplitz equation ensures the stability of Wiener Deconvolution. Both synthetic and observational seismogram checks show that Wiener Deconvolution is an effective time_domain method to estimate receiver function from teleseismic P waveform.

Novel multi–SO_(3)H functionalized ionic liquids as highly efficient catalyst for synthesis of biodiesel

Biodiesel is an attractive alternative to fossil fuels due to the energy and environmental concerns. In this paper, seven different multi –SO_(3)H functionalized ILs based on the low-cost less-substituted amines, which contained massive sites for functionalization of sulfonic acid groups and further treatment of sulfonate-based anions, were prepared as catalysts with high acidity and desirable catalytic activity for the synthesis of biodiesel from the esterification of oleic acid with methanol. The physicochemical properties of these acidic ILs were characterized by a variety of analytical techniques such as FT-IR, EA, TGA, and the Br?nsted acidity was well determined by UV–vis. Among the ILs prepared, [EDA-PS][P-TSA] showed the highest catalytic activity for esterification due to its high acidity and appropriate miscibility with reactants, with an ultrahigh97.58% conversion of oleic acid under the optimum conditions(i.e. reaction time, 1.8 h;catalyst amount, 3 wt%;alcohol/acid molar ratio, 13:1,temperature 70℃) acquired from the Box–Behnken response surface methodology. With the novel strategy of multi –SO_(3) H modification on ILs,our catalyst had an approaching or even superior oleic acid conversion rate compared to other reported catalysts with considerably lower catalyst dosage and shorter reaction time. More importantly, it also exhibited high generality for converting various FFA feedstocks into biodiesel with considerable conversion within 93.59–94.33% under a rather lower catalyst dosage, which showed the valuable potential for converting low-cost oils into biodiesel from an economic and environmental perspective.

Particle filter based on iterated importance density function and parallel resampling

The design, analysis and parallel implementation of particle filter(PF) were investigated. Firstly, to tackle the particle degeneracy problem in the PF, an iterated importance density function(IIDF) was proposed, where a new term associating with the current measurement information(CMI) was introduced into the expression of the sampled particles. Through the repeated use of the least squares estimate, the CMI can be integrated into the sampling stage in an iterative manner, conducing to the greatly improved sampling quality. By running the IIDF, an iterated PF(IPF) can be obtained. Subsequently, a parallel resampling(PR) was proposed for the purpose of parallel implementation of IPF, whose main idea was the same as systematic resampling(SR) but performed differently. The PR directly used the integral part of the product of the particle weight and particle number as the number of times that a particle was replicated, and it simultaneously eliminated the particles with the smallest weights, which are the two key differences from the SR. The detailed implementation procedures on the graphics processing unit of IPF based on the PR were presented at last. The performance of the IPF, PR and their parallel implementations are illustrated via one-dimensional numerical simulation and practical application of passive radar target tracking.

Multiquadric Radial Basis Function Approximation Scheme for Solution of Total Variation Based Multiplicative Noise Removal Model

This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.

Training of Multi-layered Neural Network for Data Enlargement Processing Using an Activity Function

In this paper, we present a study on activity functions for an MLNN (multi-layered neural network) and propose a suitable activity function for data enlargement processing. We have carefully studied the training performance of Sigmoid, ReLu, Leaky-ReLu and L & exp. activity functions for few inputs to multiple output training patterns. Our MLNNs model has L hidden layers with two or three inputs to four or six outputs data variations by BP (backpropagation) NN (neural network) training. We focused on the multi teacher training signals to investigate and evaluate the training performance in MLNNs to select the best and good activity function for data enlargement and hence could be applicable for image and signal processing (synaptic divergence) along with the proposed methods with convolution networks. We specifically used four activity functions from which we found out that L & exp. activity function can suite DENN (data enlargement neural network) training since it could give the highest percentage training abilities compared to the other activity functions of Sigmoid, ReLu and Leaky-ReLu during simulation and training of data in the network. And finally, we recommend L & exp. function to be good for MLNNs and may be applicable for signal processing of data and information enlargement because of its performance training characteristics with multiple teacher training patterns using original generated data and hence can be tried with CNN (convolution neural networks) of image processing.

Walsh Spectral Characteristics and the Auto-Correlation Function Characteristics of Forming Orthomorphic Permutations of Multi-Output Functions

Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.

Multi-factor analysis of initial poor graft function after orthotopic liver transplantation

BACKGROUND: In the early period of orthotopic liver transplantation (OLT), initial poor graft function (IPGF) is one of the complications which leads to primary graft non-function (PGNF) in serious cases. This study set out to establish the clinical risk factors resulting in IPGF after OLT. METHODS: Eighty cases of OLT were analyzed. The IPGF group consisted of patients with alanine aminotransferase (ALT) and/or aspartate aminotransferase (AST) above 1500 IU/L within 72 hours after OLT, while those in the non-IPGF group had values below 1500 IU/L. Recipient-associated factors before OLT analyzed were age, sex, primary liver disease and Child-Pugh classification; factors analyzed within the peri-operative period were non-heart beating time (NHBT), cold ischemia time (CIT), rewarming ischemic time (RWIT), liver biopsy at the end of cold ischemia; and factors analyzed within 72 hours after OLT were ALT and/or AST values. A logistic regression model was applied to filter the possible factors resulting in IPGF. RESULTS: Donor NHBT, CIT and RWIT were significantly longer in the IPGF group than in the non-IPGF group; in the logistic regression model, NHBT was the risk factor leading to IPGF (P < 0.05), while CIT and RWIT were possible risk factors. In one case in the IPGF group, PGNF appeared with moderate hepatic steatosis. CONCLUSIONS: Longer NHBT is an important risk factor leading to IPGF, while serious steatosis in the donor liver, CIT and RWIT are potential risk factors.

Relationship between Multi-Output Partially Bent Functions and Multi-Output Bent Functions

In this paper, the definition of multl-output partially Bent functions is presented and some properties are discussed. Then the relationship between multi-output partially Bent functions and multi-output Bent functions is given in Theorem 4, which includes Walsh spectrum expression and function expression. This shows that multi-output partially Bent functions and multi-output Bent functions can define each other in principle. So we obtain the general method to construct multi-output partially Bent functions from multi-output Bent functions.