Conversion from whispered speech to normal speech using the extended bilinear transformation method

A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper＇s formants in different frequency bands, the spectrum of the whispered speech will be processed in the separate partitions of this paper. On the basis of this spectrum, we will establish a conversion function able to usefully convert whispered speech to normal speech. Because of the whisper＇s non-linear offset in relation to normal speech, this paper introduces an expansion factor in the bilinear transform function making it correspond more closely to the actual conversion demands of whispered speech to normal speech. The introduction of this factor takes the non-linear move of the spectrum and the compression of the formant bandwidth into consideration, thus effectively reducing the spectrum distortion distance in the conversion. The experiment results show that the conversion presented in this paper effectively improves both the sound quality and the intelligibility of whispered speech.

Nonlocal symmetries and negative hierarchies related to bilinear Bcklund transformation

In this paper, nonlocal symmetries defined by bilinear Baacklund transformation for bilinear potential Kd V（p Kd V）equation are obtained. By introducing an auxiliary variable which just satisfies the Schwartzian form of Kd V（SKd V）equation, the nonlocal symmetry is localized and the Levi transformation is presented. Besides, based on three different types of nonlocal symmetries for potential Kd V equation, three sets of negative p Kd V hierarchies along with their bilinear forms are constructed. An impressive result is that the coefficients of the third type of（bilinear） negative p Kd V hierarchy（N 〉 0） are variable, which are obtained via introducing an arbitrary parameter by considering the translation invariance of the p Kd V equation.

Frequency Weighting Filter Design for Automotive Ride Comfort Evaluation

Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the regularities of the weighting factors,a method is proposed and the vertical and horizontal weighting filters are developed.The whole frequency range is divided several times into two parts with respective regularity.For each division,a parallel filter constituted by a low-and a high-pass filter with the same cutoff frequency and the quality factor is utilized to achieve section factors.The cascading of these parallel filters obtains entire factors.These filters own a high order.But,low order filters are preferred in some applications.The bilinear transformation method and the least P-norm optimal infinite impulse response（IIR） filter design method are employed to develop low order filters to approximate the weightings in the standard.In addition,with the window method,the linear phase finite impulse response（FIR） filter is designed to keep the signal from distorting and to obtain the staircase weighting.For the same case,the traditional method produces 0.330 7 m · s^–2 weighted root mean square（r.m.s.） acceleration and the filtering method gives 0.311 9 m · s^–2 r.m.s.The fourth order filter for approximation of vertical weighting obtains 0.313 9 m · s^–2 r.m.s.Crest factors of the acceleration signal weighted by the weighting filter and the fourth order filter are 3.002 7 and 3.011 1,respectively.This paper proposes several methods to design frequency weighting filters for automotive ride comfort evaluation,and these developed weighting filters are effective.

Traveling Wave-Guide Channels of a New Coupled Integrable Dispersionless System

In the wake of the recent investigation of new coupled integrable dispersionless equations by means of the Darboux transformation [Zhaqilao,et al.,Chin.Phys.B 18(2009) 1780],we carry out the initial value analysis of the previous system using the fourth-order Runge-Kutta's computational scheme.As a result,while depicting its phase portraits accordingly,we show that the above dispersionless system actually supports two kinds of solutions amongst which the localized traveling wave-guide channels.In addition,paying particular interests to such localized structures,we construct the bilinear transformation of the current system from which scattering amongst the above waves can be deeply studied.

A Cascade Approach to the Design of IIR Bandpass Filter

A prototype IIR bandpass filter is derived from an analog bandpass filter using bilinear transformation. The formulas relating the IIR bandpass filter's coefficients with its centre frequency and bandwidth are obtained. Using N sections of such filters, a cascade IIR bandpass filter is constructed. Based on given specifications and the formulas, the parameter N and the bandwidth of prototype filter can be obtained, and the required cascade IIR bandpass filter is obtained. The filter has a small set of coefficients with a simple structure, therefore is easy to design. The described approach is especially suitable for hardware implementation.

Implementation of Control Algorithms in Small Embedded Systems

This work describes how a control algorithm can be implemented in a small (8-bit) microcontroller for the main purpose of merging embedded systems and control theory in electrical engineering undergraduate classes. Two different methods for discretizing the control expression are compared: Euler transformation and bilinear transformation. The sampling rate’s impact on the algorithm is discussed and theoretical results are verified by an application to a temperature control system in a heating plant. Four control algorithms are compared: PID and PI algorithms discretized with Euler and bilinear transformation, respectively. It is shown that for the heating plant used in this work, a bilinear PI algorithm implemented in a small 8-bit microcontroller outperforms a commercial controller from Panasonic. It is also demonstrated that all the derived algorithms can be implemented using integer calculations only, obviating the need for expensive and time-consuming floating-point calculations. This work bridges the gap between control theory equations and the implementation of control systems in small embedded systems with no inherent floating-point processing power.

Binary Bell polynomial application in generalized(2+1)-dimensional KdV equation with variable coefficients

In this paper, we apply the binary Bell polynomial approach to high-dimensional variable-coefficient nonlinear evolution equations. Taking the generalized （2＋1）-dimensional KdV equation with variable coefficients as an illustrative example, the bilinear formulism, the bilinear Backlund transformation and the Lax pair are obtained in a quick and natural manner. Moreover, the infinite conservation laws are also derived.

Negatons, Positons, and Complexiton Solutions of Higher Order for a Non-isospectral KdV Equation

In this paper, negatons, positons, and complexiton solutions of higher order for a non-isospectral KdV equation, the KdV equation with loss and non-uniformity terms are obtained through the bilinear Baicklund transformation. Further, the properties of some solutions are shown by some figures made by using Maple.

Wronskian Form of N-Solitonic Solution for a Variable-Coefficient Korteweg-de Vries Equation with Nonuniformities

By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution in terms of Wronskian form is obtained and verified. In addition, it is shown that the （N - 1）- and N-solitonic solutions satisfy the auto-Backlund transformation through the Wronskian technique.

Integrability of an extended (2+1)-dimensional shallow water wave equation with Bell polynomials

We investigate the extended （2＋ 1）-dimensional shaUow water wave equation. The binary Bell polynomials are used to construct bilinear equation, bilinear Backlund transformation, Lax pair, and Darboux covariant Lax pair for this equation. Moreover, the infinite conservation laws of this equation are found by using its Lax pair. All conserved densities and fluxes are given with explicit recursion formulas. The N-soliton solutions are also presented by means of the Hirota bilinear method.

Study on the vehicle license plate tilt correction

The shortage of current different approaches of the vehicle license plate(VLP) tilt correction is analyzed in the paper and a new rotary correction method put forward based on the former ways of the VLP tilt correction in the horizontal direction and the vertical direction Owing to the VLP tilt taking place in the vertical direction,the array of the image’s pixels of the same column is broken,and even different rows come into being superposition.The VLP tilt taking place in the horizontal direction,by which the array of the image’s pixels of the same row broken,and so much as different columns come into being superposition.

The Modified Kadomtsev-Petviashvili Equation with Binary Bell Polynomials

Binary Bell Polynomials play an important role in the characterization of bilinear equation. The bilinear form, bilinear B?cklund transformation and Lax pairs for the modified Kadomtsev-Petviashvili equation are derived from the Binary Bell Polynomials.

Soliton Solution of the DNLS Equation Based on Hirota's Bilinear Derivative Transform

Based on the method of Hirota＇s bilinear derivative transform, the derivative nonlinear Schrodinger equation with vanishing boundary condition has been directly solved. The oneand two-soliton solutions are given as two typical examples in the illustration of the general procedures and the concrete cut-off technique of the series-form solution, and the n-soliton solution is also attained by induction method. Our study shows their equivalence to the existing soliton solutions by a simple parameter transformation. The methodological importance of bilinear derivative transform in dealing with an integrable nonlinear equation has also been emphasized. The evolution of one and two-soliton solution with respect to time and space has been discussed in detail. The collision among the solitons has been manifested through an example of two-soliton case, revealing the elastic essence of the collision and the invariance of the soliton form and characteristics.

On a Hybrid of Bilinear Hilbert Transform and Paraproduct

We introduce a class of tri-linear operators that combine features of the bilinear Hilbert transform and paraproduct. For two instances of these operators, we prove boundedness property in alarge range D ={（p1,p2,p3）ЕR3：1〈p1,p2〈∞,1/p1＋1/p2〈3/2,1〈p3〈∞}

BCKLUND TRANSFORMATION AND LAX REPRESENTATION FOR A NONLINEAR DIFFERENTIAL EQUATION

In this paper, the Hirota bilinear method is applied to a nonlinear equation which is a deformation to a KdV equation with a source. Using the Hirota’s bilinear operator, we obtain its bilinear form and construct its bilinear Bcklund transformation. And then we obtain the Lax representation for the equation from the bilinear Bcklund transformation and testify the Lax representation by the compatibility condition.

Modeling and Analysis of Interstand Tension Control in 6-high Tandem Cold Rolling Mill

The interstand tension control is one of the most important ways to meet tight tolerances for strip product quality during tandem cold rolling process. Using coordinate analysis and parabolic approximation for the mass flow balance principle, the strip velocities eliminating the use of forward slips and backward slips were calculated. In order to reduce the effect of roll eccentricity on the tension measurement, a filter based on bilinear transformation was de- signed. Applying a first-order Taylor series approximation, the transfer function matrix model of interstand tension stress was derived. The actual measurements on-site and the final calculation results showed that the established model had high calculation accuracy and was beneficial for interstand tension control of random cold rolling process.

Breathers and Rogue Waves Derived from an Extended Multi-dimensional N-Coupled Higher-Order Nonlinear Schrdinger Equation in Optical Communication Systems

In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schr¨odinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM)systems, is investigated. By the bilinear method, we construct the breather solutions for the extended (1+1),(2+1) and(3+1)-dimensional N-CHNLSE. The rogue waves are derived as a limiting form of breathers with the aid of symbolic computation. The effect of group velocity dispersion (GVD), third-order dispersion (TOD) and nonlinearity on breathers and rogue waves solutions are discussed in the optical communication systems.

Ion-acoustic wave structures in the fluid ions modeled by higher dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation

In this paper,the higher dimensional generalized Korteweg-de-Varies-Zakharov-Kuznetsov(gKdV-ZK)equation is under investigation.This model is used in the field of plasma physics which describes the effects of magnetic field on the weak ion-acoustic wave.We have applied two techniques,called asφ^(6)-model expansion method and the Hirota bilinear method(HBM)to explore the diversity of wave struc-tures.The solutions are expressed in the form of hyperbolic,periodic and Jacobi elliptic function(JEF)solutions.Moreover,the solitary wave solutions are also extracted.A comparison of our results to well-known results is made,and the study concludes that the solutions achieved here are novel.Additionally,3-dimensional and contour profiles of achieved outcomes are drawn in order to study their dynamics as a function of parameter selection.On the basis of the obtained results,we can assert that the pro-posed computational methods are straightforward,dynamic,and well-organized,and will be useful for solving more complicated nonlinear problems in a variety of fields,particularly in nonlinear sciences,in conjunction with symbolic computations.Additionally,our discoveries provide an important milestone in comprehending the structure and physical behavior of complex structures.We hope that our findings will contribute significantly to our understanding of ocean waves.This study,we hope,is appropriate and will be of significance to a broad range of experts involved in ocean engineering models.

Rational Solutions with Non-zero Asymptotics of the Modified Korteweg-de Vries Equation

Using the relation between the mKdV equation and the KdV-mKdV equation,we derive non-singular rational solutions for the mKdV equation.The solutions are given in terms of Wronskians.Dynamics of some solutions is investigated by means of asymptotic analysis.Wave trajectories of high order rational solutions are asymptotically governed by cubic curves.

Integrability and Exact Solutions of the(2+1)-dimensional KdV Equation with Bell Polynomials Approach

In this paper,the bilinear formalism,bilinear B?cklund transformations and Lax pair of the(2+1)-dimensional KdV equation are constructed by the Bell polynomials approach.The N-soliton solution is derived directly from the bilinear form.Especially,based on the two-soliton solution,the lump solution is given out analytically by taking special parameters and using Taylor expansion formula.With the help of the multidimensional Riemann theta function,multiperiodic(quasiperiodic)wave solutions for the(2+1)-dimensional KdV equation are obtained by employing the Hirota bilinear method.Moreover,the asymptotic properties of the one-and two-periodic wave solution,which reveal the relations with the single and two-soliton solution,are presented in detail.