Browsing by Subject "Interpolation"

Now showing 1 - 20 of 44

Open Access
Accurate plane-wave excitation in the FDTD method
(IEEE, 1997) Gürel, Levent; Oğuz, Uğur; Arıkan, Orhan
Different techniques are developed to implement plane-wave excitation on the finite-difference time-domain (FDTD) method, such as the initial-condition, the hard-source, and the connecting-condition techniques, for the total-field/scattered field (TF/SF) formulation. In the TF/SF formulation, the incident field is computed and fed to the 3D FDTD grid on the boundary separating the total-field and the scattered-field regions. Since the incedent field is a known quantity, a closed-form expression can be evaluated on every point of this boundary. A more efficient way of computing the incedent field is by using an incedent-field array (IFA), which is a 1D FDTD grid set-up to numerically propagate the incedent field into the 3D FDTD.
Open Access
Adaptive correction and look-up table based interpolation of quadrature encoder signals
(ASME, 2012-10) Ulu, Erva; Geçer-Ulu, Nurcan; Çakmakçı, Melih
This paper presents a new method to increase the available measurement resolution of quadrature encoder signals. The proposed method features an adaptive signal correction phase and an interpolation phase. Typical imperfections in the encoder signals including amplitude difference, mean offsets and quadrature phase shift errors are corrected using recursive least squares with exponential forgetting and resetting. Interpolation of the corrected signals are accomplished by a quick access look-up table formed offline to satisfy a linear mapping from available sinusoidal signals to higher order sinusoids. The position information can be derived from the conversion of the high-order sinusoids to binary pulses. With the presented method, 10nm resolution is achieved with an encoder having 1μm of original resolution. Further increase in resolution can also be satisfied with minimizing electrical noises. Experiment results demonstrating the effectiveness of the proposed method for a single axis and two axis slider systems are given. Copyright © 2012 by ASME.
Open Access
Computation of holographic patterns between tilted planes
(SPIE - International Society for Optical Engineering, 2006-05) Esmer, Gökhan Bora; Onural, Levent
Computation of the diffraction pattern that gives the desired reconstruction of an object upon proper illumination is an important process in computer generated holography. A fast computational method, based on the plane wave decomposition of 3D field in free-space, is presented to find the desired diffraction pattern. The computational burden includes two FFT algorithms in addition to a shuffling of the frequency components that needs an interpolation in the frequency domain. The algorithm is based on the exact diffraction formulation; there is no need for Fresnel or Fraunhofer approximations. The developed model is utilized to calculate the scalar optical diffraction between tilted planes for monochromatic light. The performance of the presented algorithm is satisfactory for tilt angles up to 60°.
Open Access
DCT coding of nonrectangularly sampled images
(IEEE, 1994) Gündüzhan, E.; Çetin, A. Enis; Tekalp, A. M.
Discrete cosine transform (DCT) coding is widely used for compression of rectangularly sampled images. In this letter, we address efficient DCT coding of nonrectangularly sampled images. To this effect, we discuss an efficient method for the computation of the DCT on nonrectangular sampling grids using the Smith-normal decomposition. Simulation results are provided.
Open Access
Delay margin optimization for systems with ınternal delayed feedback
(Elsevier, 2021-07-16) Özbay, Hitay
In this brief paper, controller design for delay margin optimization is considered for systems with internal feedback delays (systems with delays in the state variables). Similar to existing results on delay margin optimization for finite dimensional systems with I/O delays, it is shown that the problem considered can be solved by using Nevanlinna-Pick interpolation involving non-minimum phase zeros of the plant.
Open Access
Discrete scaling based on operator theory
(Elsevier, 2020-11-04) Koç, Aykut; Bartan, B.; Özaktaş, Haldun Memduh
Signal scaling is a fundamental operation of practical importance in which a signal is made wider or narrower along the coordinate direction(s). Scaling, also referred to as magnification or zooming, is complicated for signals of a discrete variable since it cannot be accomplished simply by moving the signal values to new coordinate points. Most practical approaches to discrete scaling involve interpolation. We propose a new approach based on hyperdifferential operator theory that does not involve conventional interpolation. This approach provides a self-consistent and pure definition of discrete scaling that is fully consistent with discrete Fourier transform theory. It can potentially be applied to other problems in signal theory and analysis such as transform designs. Apart from its theoretical elegance, it also provides a basis for numerical implementation.
Open Access
The effect of distribution of information on recovery of propagating signals
(2015-09) Karabulut, Özgecan
Interpolation is one of the fundamental concepts in signal processing. The analysis of the di fficulty of interpolation of propagating waves is the subject of this thesis. It is known that the information contained in a propagating wave fi eld can be fully described by its uniform samples taken on a planar surface transversal to the propagation direction, so the eld can be found anywhere in space by using the wave propagation equations. However in some cases, the sample locations may be irregular and/or nonuniform. We are concerned with interpolation from such samples. To be able to reduce the problem to a pure mathematical form, the fractional Fourier transform is used thanks to the direct analogy between wave propagation and fractional Fourier transformation. The linear relationship between each sample and the unknown field distribution is established this way. These relationships, which constitute a signal recovery problem based on multiple partial fractional Fourier transform information, are analyzed. Recoverability of the fi eld is examined by comparing the condition numbers of the constructed matrices corresponding to di fferent distributions of the available samples.
Open Access
An efficient and accurate technique for the incident-wave excitations in the FDTD method
(Institute of Electrical and Electronics Engineers, 1998-06) Oğuz, U.; Gürel, Levent; Arıkan, Orhan
An efficient technique to improve the accuracy of the finite-difference time-domain (FDTD) solutions employing incident-wave excitations is developed. In the separate-field formulation of the FDTD method, any incident wave may be efficiently introduced to the three-dimensional (3-D) computational domain by interpolating from a one-dimensional (1-D) incident-field array (IFA), which is a 1-D FDTD grid simulating the propagation of the incident wave. By considering the FDTD computational domain as a sampled system and the interpolation operation as a decimation process, signal-processing techniques are used to identify and ameliorate the errors due to aliasing. The reduction in the error is demonstrated for various cases. This technique can be used for the excitation of the FDTD grid by any incident wave. A fast technique is used to extract the amplitude and the phase of a sampled sinusoidal signal.
Open Access
Energy and mass of 3D and 2D polarons in the overall range of the electron-phonon coupling strength
(Institute of Physics Publishing Ltd., 1994) Ercelebi, A.; Senger, R. T.
The ground-state characterization of the polaron problem is retrieved within the framework of a variational scheme proposed previously by Devreese et al for the bound polaron. The formulation is based on the standard canonical transformation of the strong coupling ansatz and consists of a variationally determined perturbative extension serving for the theory to interpolate in the overall range of the coupling constant. Specializing our considerations to the bulk and strict two-dimensional polaron models we see that the theory yields significantly improved energy upper bounds in the strong coupling regime and, moreover, extrapolates itself successfully towards the well-established weak coupling limits for all polaron quantities of general interest.
Open Access
Fast and accurate solutions of large-scale scattering problems with parallel multilevel fast multipole algorithm
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
Fast and accurate solution of large-scale scattering problems obtained by integral-equation formulations for conducting surfaces is considered in this paper. By employing a parallel implementation of the multilevel fast multipole algorithm (MLFMA) on relatively inexpensive platforms. Specifically, the solution of a scattering problem with 33,791,232 unknowns, which is even larger than the 20-million unknown problem reported recently. Indeed, this 33-million-unknown problem is the largest integral-equation problem solved in computational electromagnetics.
Open Access
Fractional free space, fractional lenses, and fractional imaging systems
(OSA - The Optical Society, 2003) Sümbül, U.; Özaktaş, Haldun M.
Continuum extensions of common dual pairs of operators are presented and consolidated, based on the fractional Fourier transform. In particular, the fractional chirp multiplication, fractional chirp convolution, and fractional scaling operators are defined and expressed in terms of their common nonfractional special cases, revealing precisely how they are interpolations of their conventional counterparts. Optical realizations of these operators are possible with use of common physical components. These three operators can be interpreted as fractional lenses, fractional free space, and fractional imaging systems, respectively. Any optical system consisting of an arbitrary concatenation of sections of free space and thin lenses can be interpreted as a fractional imaging system with spherical reference surfaces. As a special case, a system departing from the classical single-lens imaging condition can be interpreted as a fractional imaging system. © 2003 Optical Society of America.
Open Access
Harmonic Besov spaces on the ball
(World Scientific Publishing, 2016) Gergün, S.; Kaptanoğlu, H. T.; Üreyen, A. E.
We initiate a detailed study of two-parameter Besov spaces on the unit ball of ℝn consisting of harmonic functions whose sufficiently high-order radial derivatives lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels are weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. Estimates of the growth of kernels lead to characterization of integral transformations on Lebesgue classes. The transformations allow us to conclude that the order of the radial derivative is not a characteristic of a Besov space as long as it is above a certain threshold. Using kernels, we define generalized Bergman projections and characterize those that are bounded from Lebesgue classes onto Besov spaces. The projections provide integral representations for the functions in these spaces and also lead to characterizations of the functions in the spaces using partial derivatives. Several other applications follow from the integral representations such as atomic decomposition, growth at the boundary and of Fourier coefficients, inclusions among them, duality and interpolation relations, and a solution to the Gleason problem. © 2016 World Scientific Publishing Company.
Open Access
Input sequence estimation and blind channel identification in HF communication
(IEEE, 2000) Khames, Mariam; Miled, B. H.; Arıkan, Orhan
A new algorithm is proposed for reliable communication over HF tropospheric links in the presence of rapid channel variations. In the proposed approach, using fractionally space channel outputs, sequential estimation of channel characteristics and input sequence is performed by utilizing subspace tracking and Kalman filtering. Simulation based comparisons with the existing algorithms show that the proposed approaches significantly improve the performance of the communication system and enable us to utilize HF communication in bad conditions.
Open Access
Interpolating between periodicity and discreteness through the fractional Fourier transform
(IEEE, 2006) Özaktaş, H. M.; Sümbül, U.
Periodicity and discreteness are Fourier duals in the same sense as operators such as coordinate multiplication and differentiation, and translation and phase shift. The fractional Fourier transform allows interpolation between such operators which gradually evolve from one member of the dual pair to the other as the fractional order goes from zero to one. Here, we similarly discuss the interpolation between the dual properties of periodicity and discreteness, showing how one evolves into the other as the order goes from zero to one. We also discuss the concepts of partial discreteness and partial periodicity and relate them to fractional discreteness and periodicity. © 2006 IEEE.
Open Access
Interpolation for completely positive maps: Numerical solutions
(Societatea de Stiinte Matematice din Romania, 2018) Ambrozie, C.; Gheondea, Aurelian
We present a few techniques to find completely positive maps between full matrix algebras taking prescribed values on given data, based on semidefinite programming, convex minimization supported by a numerical example, as well as representations by linear functionals. The particular case of commutative data is also discussed.
Open Access
An interpolation problem for completely positive maps on matrix algebras: solvability and parametrization
(Taylor & Francis, 2015) Ambrozie, C. G.; Gheondea, A.
We present certain existence criteria and parameterizations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed matrices. Our approach uses density matrices associated to linear functionals on (Formula presented.) -subspaces of matrices, inspired by the Smith-Ward linear functional and Arveson’s Hahn-Banach Type Theorem. A necessary and sufficient condition for the existence of solutions and a parametrization of the set of all solutions of the interpolation problem in terms of a closed and convex set of an affine space are obtained. Other linear affine restrictions, like trace preserving, can be included as well, hence covering applications to quantum channels that yield certain quantum states at prescribed quantum states. We also perform a careful investigation on the intricate relation between the positivity of the density matrix and the positivity of the corresponding linear functional.
Open Access
Interpolation techniques to improve the accuracy of the plane wave excitations in the finite difference time domain method
(Wiley-Blackwell Publishing, Inc., 1997-11) Oğuz, U.; Gürel, Levent
The importance of matching the phase velocity of the incident plane wave to the numerical phase velocity imposed by the numerical dispersion of the three-dimensional (3-D) finite difference time domain (FDTD) grid is demonstrated. In separate-field formulation of the FDTD method, a plane wave may be introduced to the 3-D computational domain either by evaluating closed-form incident-field expressions or by interpolating from a 1-D incident-field array (IFA), which is a 1-D FDTD grid simulating the propagation of the plane wave. The relative accuracies and efficiencies of these two excitation schemes are compared, and it has been shown that higher-order interpolation techniques can be used to improve the accuracy of the IFA scheme, which is already quite efficient.
Open Access
İyonosfer TEİ verilerinin uzay-zamansal aradeğerlemesi
(IEEE, 2011-04) Yıldız, Aykut; Arıkan, Orhan; Arıkan, F.
GPS sinyalleri iyonosferdeki elektron yoğunluğunun kestirilmesi için önemli bir bilgi kaynağıdır. Ancak, GPS alıcılarında sinyallerin kaydedilemediği durumlar olmaktadır. Bu kesinti sırasında iyonosfer elektron içeriğinin kestiriminin yapılabilmesi için kesinti sureleri içinde kalan verilerin aradeğerleme ile kestirimi gereklidir. Bu çalışmada, bir GPS ağındaki ölçümlerin uzay-zamansal ilintileri kullanılarak yeni bir aradeğerleme tekniği geliştirilmiştir. Gerçek veriye dayalı sonuçlar, geliştirilen tekniğin yüksek başarımlı kestirimler ürettiğini göstermiştir. GPS signals are crucial, because they are used to estimate the electron density in the ionosphere. However, sometimes GPS receivers can not receive signals. In order to estimate ionospheric electron density during this cutoff, the interpolation of the data is necessary. In this paper, a new interpolation scheme that uses spatio-temporal correlation in the GPS network is proposed. The simulation results on real data show that the proposed technique produces promising results. © 2011 IEEE.
Open Access
Klasik yunanca ve latince metinlerde görülen bozulmaların nedenleri
(Türk Eskiçağ Bilimleri Enstitüsü, 2015) Asuman, Coşkun-Abuagla
Ortaçağa gelinceye kadar antik Yunanca ve Latince metinler, sözcükler arasında boşluk bıra-kılmadan yazılmış ve kopya edilmiştir. Bunun yanı sıra Hellenistik Döneme kadar Yunanca metinlerde vurgu sistemi kullanılmamış, vurgu işaretlerinin yazılması için bir sistem bulun-duktan sonra bile bu sistem, Ortaçağın ilk yarısına kadar hayata geçirilmemiştir. Söz konusu bu iki neden, yazıcıların dikkatlerinin kolayca dağılmasına ve kopya ettikleri antik metinlerin ciddi şekilde bozulmasına neden olmuştur. Hellenistik Dönem öncesinde başlayan, özellikle Ortaçağda metni asıl haline getirmek için düzeltme (emendatio) çabasıyla ya da metne yeni sözcükler ve parçalar ekleyip metnin aslını bozmakla (interpolatio) içinden çıkılmaz bir durum alan, metin bozulmalarının en önemli nedenlerinden biri çoğu yazıcının isteyerek ya da iste-meyerek önündeki metnin doğru ve eksiksiz kopyasını yapmakta yetersiz oluşudur. Bu kişilerin sık sık dikkatlerinin dağılması ilk bakışta şaşırtıcı gelse de kısa bir metnin bile eksiksiz ve birebir kopyasını yapmanın ne kadar zor ve zahmetli bir iş olduğu bu işin uzmanları tarafından iyi bilinir. Bu makalenin amacı antik metinlerde görülen bozulmaların nedenlerine ilişkin kısa bir bilgi vermektir.
Open Access
Linear algebraic analysis of fractional Fourier domain interpolation
(IEEE, 2009) Öktem, Figen S.; Özaktaş, Haldun M.
In this work, we present a novel linear algebraic approach to certain signal interpolation problems involving the fractional Fourier transform. These problems arise in wave propagation, but the proposed approach to these can also be applicable to other areas. We see this interpolation problem as the problem of determining the unknown signal values from the given samples within some tolerable error. We formulate the problem as a linear system of equations and use the condition number as a measure of redundant information in given samples. By analyzing the effect of the number of known samples and their distributions on the condition number with simulation examples, we aim to investigate the redundancy and information relations between the given data.