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This paper provides a semi analytical procedure to factorize the two dimensional kernel involved in the quarter plane diffraction problem. The proposed method is based on the reduction of the factorization problem to the solution of a Fredholm integral equation of second kind. The solution of the Fredholm integral equation appears cumbersome since it involves two folded integrals. In order to reduce...
A theorem is formulated and substantiated numerically, stating that if λm, n(v) is the n th zero of the generalized Laguerre polynomial Lm(v)(X) (x and λm, n(v) - real, positive, v =0,1,2,..., m =0,1,2,..., n =1,2,3...) and L(c, n) (c =1,2,3,...) is a positive real number, defined by means of the relation: L(c, n) =k_→-∞lim K_(c, n, k_) = k_→-∞lim M_(c, n, k_) in which K_(c, n, k_) = |k_|ζ(c)k_, n...
This paper makes use of local polynomial Wigner-Ville distribution (LPWVD), originally designed for nonparametric instantaneous frequency (IF) estimation of transient signals, to propose a parametric IF estimation for polynomial phase signals (PPSs). Statistical performance such as asymptotic bias and variance of the LPWVD-based parametric IF estimator is derived in closed-form. Based on the analytical...
A new set of hierarchical vector basis functions that spans the curl-conforming reduced-gradient spaces of Nédélec on a triangular-prism cell is presented. These functions are constructed from orthogonal scalar polynomials to enhance their linear independence, which is a simpler process than an orthogonalization applied to the final vector functions. The new functions are compatible with those recently...
This paper compares two different solutions to the problem of scattering by a perfectly conducting square plate illuminated by a normally incident plane wave. The first one is an accurate numerical solution intended to serve as benchmark, while the second is an accurate solution obtained from the truncation of an exact analytical solution.
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