Browsing by Subject "Orthogonality"
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Item Open Access Spherical wave representation of the dyadic Green's function for a spherical impedance boss at the edge of a perfectly conducting wedge(Electromagnetics Academy, 2012) Ghassemiparvin, Behnam; Altıntaş, AyhanIn this work, canonical problem of a scatterer at the edge of a wedge is considered and eigenfunction solution is developed. Initially, a dyadic Green's function for a spherical impedance boss at the edge of a perfect electrically conducting (PEC) wedge is obtained. Since scattering from objects at the edge is of interest, a three-dimensional Green's function is formulated in terms of spherical vector wave functions. First, an incomplete dyadic Green's function is expanded in terms of solenoidal vector wave functions with unknown coefficients, which is not valid in the source region. Unknown coefficients are calculated by utilizing the Green's second identity and orthogonality of the vector wave functions. Then, the solution is completed by adding general source correction term. Resulting Green's function is decomposed into two parts. First part is the dyadic Green's function of the wedge in the absence of the sphere and the second part represents the effects of the spherical boss and the interaction between the wedge and the scatterer. In contrast to cylindrical vector wave function expansions and asymptotic solutions which fail to converge in the paraxial region, proposed solution exhibits good convergence everywhere in space. Using the developed Green's function scattered field patterns are obtained for several impedance values and results are compared with those of a PEC spherical boss. Effects of the incident angle and surface impedance of the boss on the scattering pattern are also examined.Item Open Access Ultra-wideband orthogonal pulse shape set design by using Hermite-Gaussian functions(IEEE, 2012) Alp, Yaşar Kemal; Dedeoǧlu, Mehmet; Arıkan, OrhanUltra-Wideband (UWB) communication systems have been developed for short distance, high data rate communications. To avoid interfering with the existing systems in the same environment, very short duration pulses used by these systems should satisfy a predefined spectral mask. Data rate of UWB systems can be increased by using multiple pulse shapes simultaneously. Orthogonality of the simultaneously used pulse shapes simplifies the receiver design. In this work, design of orthogonal pulse shapes which satisfy the spectral mask is modelled as an optimization problem. First, it is converted to a convex optimization problem by constraining the pulse shapes to lie in a subspace spanned by the Hermite-Gaussian (HG) functions. Then the optimal solution is obtained. It is shown that a larger pulse shape set can be designed compared to the existing approaches, and hence, a higher data rate can be achieved. © 2012 IEEE.