Small Number Of Sampling Points Research Articles

Iterative inverse filtering approach to the estimation of frequencies of noisy sinusoids

A signal modeling approach is proposed to reduce the problem of estimating frequencies of noisy sinusoids to the parameter estimation problem. Both white and colored noise are considered. The maximum likelihood approach leads to an algorithm computationally inefficient for low values of signal-to-noise ratio. Based on the equation-error formulation, an iterative inverse filtering algorithm is derived in the case of colored noise, and a generalized least-squares algorithm in the case of white noise. It is shown, on the basis of numerous experimental results, that the iterative inverse filtering algorithm provides highly accurate estimates of unknown frequencies for low values of signal-to-noise ratio, even in the case of a small number of sampling points.

Gaussian Quadrature Xα Method for Self-Consistent Hartree-Fock-Slater Equation. I. Application to the Total Energy Calculation of Diatomic Molecule

In order to improve the accuracy for the Diophantine integration scheme in the discrete variational X α method, which makes orbital calculations with non muffin-tin potential for large systems, it is proposed to use Gaussian quadrature (GQ) for integrating the Hamiltonian and overlap matrix elements. The values for these quantities show very good convergence with a relatively small number of sampling points. The total energy calculations as well as orbital energy calculations are carried out for diatomic CO and C 2 molecules. The calculated dissociation energies reasonably agree with experimental data. Equilibrium bond distances, however, are somewhat larger than the experimental value. The present method has been applied to diatomic FeO molecule. The bond distance and bond energy for this molecule are discussed.

Special points for the evaluation of form factors and Fourier series representations in hexagonal crystals

Efficient Gaussian type formulae are developed for evaluating the Fourier coefficients (form factors) of symmetrized plane waves for a hexagonal close-packed system in both real and reciprocal space ([Formula: see text] and [Formula: see text], respectively). These are the most efficient possible for a small number of sample points and represent a major advance over previous work on special point formulae. They will be particularly powerful for performing calculations of surface properties. The convergence of a Fourier series representation of energy bands is investigated by use of these formulae and found to converge slowly.