In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a pol...In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a polynomial equation with integer coefficients quickly based on this result.展开更多
Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA's gain and phase errors both in far and near fields are proposed. In the far field, using a single sound so...Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA's gain and phase errors both in far and near fields are proposed. In the far field, using a single sound source without exact orientation, this method horizontally rotates the array exactly once, performs eigen value decomposition for the covariance matrix of received data, then computes the gain and phase error according to the formulas. In the near field, using the same single sound source, it is necessary to rotate the array horizontally at most three times, build equations according to geometric relations, then solve them. Using the formula proposed in this paper, spherical waves are modified into plane waves. Then eigen values decomposition is performed. These two calibration methods were shown to be valid by simulation and are fast, accurate and easy to use. Finally, an analysis of factors influencing estimation precision is given.展开更多
This paper addresses an algebraic approach for wideband frequency estimation with sub-Nyquist temporal sampling. Firstly, an algorithm based on double polynomial root finding procedure to estimate aliasing frequencies...This paper addresses an algebraic approach for wideband frequency estimation with sub-Nyquist temporal sampling. Firstly, an algorithm based on double polynomial root finding procedure to estimate aliasing frequencies and joint aliasing frequencies-time delay phases in multi-signal situation is presentcd. Since the sum of time delay phases determined from the least squares estimation shows the characteristics of the corre- sponding parameters pairs, then the pairmatching method is conducted by combining it with estimated parameters mentioned above. Although the proposed method is computationally simpler than the conventional schemes, simulation results show that it can approach optimum estimation performance.展开更多
The localized differential quadrature (LDQ) method is a numerical technique with high accuracy for solving most kinds of nonlinear problems in engineering and can overcome the difficulties of other methods (such as di...The localized differential quadrature (LDQ) method is a numerical technique with high accuracy for solving most kinds of nonlinear problems in engineering and can overcome the difficulties of other methods (such as difference method) to numerically evaluate the derivatives of the functions.Its high efficiency and accuracy attract many engineers to apply the method to solve most of the numerical problems in engineering.However,difficulties can still be found in some particular problems.In the following study,the LDQ was applied to solve the Sod shock tube problem.This problem is a very particular kind of problem,which challenges many common numerical methods.Three different examples were given for testing the robustness and accuracy of the LDQ.In the first example,in which common initial conditions and solving methods were given,the numerical oscillations could be found dramatically;in the second example,the initial conditions were adjusted appropriately and the numerical oscillations were less dramatic than that in the first example;in the third example,the momentum equation of the Sod shock tube problem was corrected by adding artificial viscosity,causing the numerical oscillations to nearly disappear in the process of calculation.The numerical results presented demonstrate the detailed difficulties encountered in the calculations,which need to be improved in future work.However,in summary,the localized differential quadrature is shown to be a trustworthy method for solving most of the nonlinear problems in engineering.展开更多
文摘In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a polynomial equation with integer coefficients quickly based on this result.
文摘Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA's gain and phase errors both in far and near fields are proposed. In the far field, using a single sound source without exact orientation, this method horizontally rotates the array exactly once, performs eigen value decomposition for the covariance matrix of received data, then computes the gain and phase error according to the formulas. In the near field, using the same single sound source, it is necessary to rotate the array horizontally at most three times, build equations according to geometric relations, then solve them. Using the formula proposed in this paper, spherical waves are modified into plane waves. Then eigen values decomposition is performed. These two calibration methods were shown to be valid by simulation and are fast, accurate and easy to use. Finally, an analysis of factors influencing estimation precision is given.
文摘This paper addresses an algebraic approach for wideband frequency estimation with sub-Nyquist temporal sampling. Firstly, an algorithm based on double polynomial root finding procedure to estimate aliasing frequencies and joint aliasing frequencies-time delay phases in multi-signal situation is presentcd. Since the sum of time delay phases determined from the least squares estimation shows the characteristics of the corre- sponding parameters pairs, then the pairmatching method is conducted by combining it with estimated parameters mentioned above. Although the proposed method is computationally simpler than the conventional schemes, simulation results show that it can approach optimum estimation performance.
文摘The localized differential quadrature (LDQ) method is a numerical technique with high accuracy for solving most kinds of nonlinear problems in engineering and can overcome the difficulties of other methods (such as difference method) to numerically evaluate the derivatives of the functions.Its high efficiency and accuracy attract many engineers to apply the method to solve most of the numerical problems in engineering.However,difficulties can still be found in some particular problems.In the following study,the LDQ was applied to solve the Sod shock tube problem.This problem is a very particular kind of problem,which challenges many common numerical methods.Three different examples were given for testing the robustness and accuracy of the LDQ.In the first example,in which common initial conditions and solving methods were given,the numerical oscillations could be found dramatically;in the second example,the initial conditions were adjusted appropriately and the numerical oscillations were less dramatic than that in the first example;in the third example,the momentum equation of the Sod shock tube problem was corrected by adding artificial viscosity,causing the numerical oscillations to nearly disappear in the process of calculation.The numerical results presented demonstrate the detailed difficulties encountered in the calculations,which need to be improved in future work.However,in summary,the localized differential quadrature is shown to be a trustworthy method for solving most of the nonlinear problems in engineering.
