Browsing by Subject "Sampling"

Now showing 1 - 20 of 20

Open Access
Accounting for parameter uncertainty in large-scale stochastic simulations with correlated inputs
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2011) Biller, B.; Corlu, C. G.
This paper considers large-scale stochastic simulations with correlated inputs having normal-to-anything (NORTA) distributions with arbitrary continuous marginal distributions. Examples of correlated inputs include processing times of workpieces across several workcenters in manufacturing facilities and product demands and exchange rates in global supply chains. Our goal is to obtain mean performance measures and confidence intervals for simulations with such correlated inputs by accounting for the uncertainty around the NORTA distribution parameters estimated from finite historical input data. This type of uncertainty is known as the parameter uncertainty in the discrete-event stochastic simulation literature. We demonstrate how to capture parameter uncertainty with a Bayesian model that uses Sklar's marginal-copula representation and Cooke's copula-vine specification for sampling the parameters of the NORTA distribution. The development of such a Bayesian model well suited for handling many correlated inputs is the primary contribution of this paper. We incorporate the Bayesian model into the simulation replication algorithm for the joint representation of stochastic uncertainty and parameter uncertainty in the mean performance estimate and the confidence interval. We show that our model improves both the consistency of the mean line-item fill-rate estimates and the coverage of the confidence intervals in multiproduct inventory simulations with correlated demands.
Open Access
Application of signal-processing techniques to reduce the errors related to the FDTD excitations
(IEEE, 2001) Gürel, Levent; Oğuz, Uğur
A study on the reduction of the errors related to the finite-difference time-domain (FDTD) excitations was performed by employing signal-processing techniques. Plane-wave scattering problems were simulated. The improvements in both plane-wave and finite-source excitation schemes were demonstrated. The result showed that a visible DC offset value was exhibited even after five periods of the incident wave.
Open Access
A aurvey of signal processing problems and tools in holographic three-dimensional television
(Institute of Electrical and Electronics Engineers, 2007) Onural, L.; Gotchev, A.; Özaktaş, Haldun M.; Stoykova, E.
Diffraction and holography are fertile areas for application of signal theory and processing. Recent work on 3DTV displays has posed particularly challenging signal processing problems. Various procedures to compute Rayleigh-Sommerfeld, Fresnel and Fraunhofer diffraction exist in the literature. Diffraction between parallel planes and tilted planes can be efficiently computed. Discretization and quantization of diffraction fields yield interesting theoretical and practical results, and allow efficient schemes compared to commonly used Nyquist sampling. The literature on computer-generated holography provides a good resource for holographic 3DTV related issues. Fast algorithms to compute Fourier, Walsh-Hadamard, fractional Fourier, linear canonical, Fresnel, and wavelet transforms, as well as optimization-based techniques such as best orthogonal basis, matching pursuit, basis pursuit etc., are especially relevant signal processing techniques for wave propagation, diffraction, holography, and related problems. Atomic decompositions, multiresolution techniques, Gabor functions, and Wigner distributions are among the signal processing techniques which have or may be applied to problems in optics. Research aimed at solving such problems at the intersection of wave optics and signal processing promises not only to facilitate the development of 3DTV systems, but also to contribute to fundamental advances in optics and signal processing theory.
Open Access
Automatic detection of compound structures by joint selection of region groups from a hierarchical segmentation
(Institute of Electrical and Electronics Engineers, 2016) Akçay, H. G.; Aksoy, S.
A challenging problem in remote sensing image analysis is the detection of heterogeneous compound structures such as different types of residential, industrial, and agricultural areas that are composed of spatial arrangements of simple primitive objects such as buildings and trees. We describe a generic method for the modeling and detection of compound structures that involve arrangements of an unknown number of primitives in large scenes. The modeling process starts with a single example structure, considers the primitive objects as random variables, builds a contextual model of their arrangements using a Markov random field, and learns the parameters of this model via sampling from the corresponding maximum entropy distribution. The detection task is formulated as the selection of multiple subsets of candidate regions from a hierarchical segmentation where each set of selected regions constitutes an instance of the example compound structure. The combinatorial selection problem is solved by the joint sampling of groups of regions by maximizing the likelihood of their individual appearances and relative spatial arrangements. Experiments using very high spatial resolution images show that the proposed method can effectively localize an unknown number of instances of different compound structures that cannot be detected by using spectral and shape features alone.
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
Diffraction and holography from a signal processing perspective
(SPIE, 2006) Onural, Levent; Özaktaş, Haldun M.
The fact that plane waves are solutions of the Helmholtz equation in free space allows us to write the exact solution to the diffraction problem as a superposition of plane waves. The solution of other related problems can also be expressed in similar forms. These forms are very well suited for directly importing various signal processing tools to diffraction related problems. Another signal processing-diffraction link is the application of novel sampling theorems and procedures in signal processing to diffraction for the purpose of more convenient and efficient discrete representation and the use of associated computational algorithms. Another noteworthy link between optics and signal processing is the fractional Fourier transform. Revisiting diffraction from a modern signal processing perspectiv is likely to yield both interesting viewpoints and improved techniques.
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
Efficient computation of the ambiguity function and the Wigner distribution on arbitrary line segments
(IEEE, Piscataway, NJ, United States, 1999) Özdemir, A. K.; Arıkan, Orhan
Efficient algorithms are proposed for the computation of Wigner distribution and ambiguity function samples on arbitrary line segments based on the relationship of Wigner distribution and ambiguity function with the fractional Fourier transformation. The proposed algorithms make use of an efficient computation algorithm of fractional Fourier transformation to compute N uniformly spaced samples O(N log N) flops. The ability of obtaining samples on arbitrary line segments provides significant freedom in the shape of the grids used in the Wigner distribution or in ambiguity function computations.
Open Access
Finite representation of finite energy signals
(2011) Gülcü, Talha Cihad
In this thesis, we study how to encode finite energy signals by finitely many bits. Since such an encoding is bound to be lossy, there is an inevitable reconstruction error in the recovery of the original signal. We also analyze this reconstruction error. In our work, we not only verify the intuition that finiteness of the energy for a signal implies finite degree of freedom, but also optimize the reconstruction parameters to get the minimum possible reconstruction error by using a given number of bits and to achieve a given reconstruction error by using minimum number of bits. This optimization leads to a number of bits vs reconstruction error curve consisting of the best achievable points, which reminds us the rate distortion curve in information theory. However, the rate distortion theorem are not concerned with sampling, whereas we need to take sampling into consideration in order to reduce the finite energy signal we deal with to finitely many variables to be quantized. Therefore, we first propose a finite sample representation scheme and question the optimality of it. Then, after representing the signal of interest by finite number of samples at the expense of a certain error, we discuss several quantization methods for these finitely many samples and compare their performances.
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
A multiresolution nonrectangular wavelet representation for two-dimensional signals
(Elsevier, 1993) Çetin, A. Enis
In this paper, a new multiresolution wavelet representation for two-dimensional signals is described. This wavelet representation is based on a nonrectangular decomposition of the frequency domain. The decomposition can be implemented by a digital filter bank. The application of the new representation to the coding of quincunx and rectangularly sampled images is considered and simulation examples are presented.
Open Access
Optimal representation and processing of optical signals in quadratic-phase systems
(Elsevier, 2016) Arik, S. Ö.; Özaktaş, Haldun M.
Optical fields propagating through quadratic-phase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. Non-redundant representation of the fields with the minimum number of samples becomes possible by appropriate choice of sample points on these surfaces. Longitudinally, these surfaces should not be spaced equally with the distance of propagation, but with respect to the FRT order. The non-uniform sampling grid that emerges mirrors the fundamental structure of propagation through QPSs. By providing a means to effectively handle the sampling of chirp functions, it allows for accurate and efficient computation of optical fields propagating in QPSs.
Open Access
Reducing the dispersion errors of the finite-difference time-domain method for multifrequency plane-wave excitations
(Taylor & Francis, 2003) Oğuz, U.; Gürel, Levent
We demonstrate the applications of discrete-time signal-processing (SP) techniques for the purpose of generating accurate plane waves in the finite-difference time-domain (FDTD) method. The SP techniques are used either to reduce the high-frequency content of the source excitation or to compute more precise incident-field values in the computational domain. The effects of smoothing windows of various lengths, digital lowpass filters of various bandwidths and characteristics, and polynomial interpolation schemes of various orders are investigated. Arbitrary signals with multifrequency content are considered.
Embargo
Relationships between two definitions of the discrete Wigner distribution and the continuous Wigner distribution
(Elsevier, 2025-03) Korkmaz, Sayit; Özaktaş, Haldun M.
We present a very simple relationship between two widely used discrete-time discrete-frequency Wigner distributions. The first one is obtained through sampling and the second one is obtained from the representation theory of the finite Heisenberg group. This relation shows that the values of one can simply be obtained by permuting the values of the other along the frequency axis, which in turn implies a relationship of the second definition to the samples of the continuous Wigner distribution, and the first definition to group representation theory. In the process, we derive a simplified form for the second definition which is completely analogous to the continuous Wigner distribution, and develop a set of relationships relating this definition to a discrete ambiguity function and auxiliary functions.
Open Access
Sampling and series expansion theorems for fractional Fourier and other transforms
(Elsevier, 2003) Candan, Ç.; Özaktaş, Haldun M.
The sampling and series expansion theorems for fractional Fourier transforms were analyzed. In addition to the fractional Fourier transform, the method can also be applied to the Fresnel, Hartley and scale transforms. The technique could also be useful as a generic tool which can produce key relations systematically in a few steps.
Open Access
Signal processing issues in diffraction and holographic 3DTV
(Elsevier BV, 2007) Onural, L.; Özaktaş, Haldun M.
Image capture and image display will most likely be decoupled in future 3DTV systems. Due to the need to convert abstract representations of 3D images to display driver signals, and to explicitly consider optical diffraction and propagation effects, it is expected that signal processing issues will be of fundamental importance in 3DTV systems. Since diffraction between two parallel planes can be represented as a 2D linear shift-invariant system, various signal processing techniques naturally play an important role. Diffraction between tilted planes can also be modeled as a relatively simple system, leading to efficient discrete computations. Two fundamental problems are digital computation of the optical field arising from a 3D object, and finding the driver signals for a given optical display device which will then generate a desired optical field in space. The discretization of optical signals leads to several interesting issues; for example, it is possible to violate the Nyquist rate while sampling, but still achieve full reconstruction. The fractional Fourier transform is another signal processing tool which finds applications in optical wave propagation.
Open Access
Signal-processing techniques to reduce the sinusoidal steady-state error in the FDTD method
(IEEE, 2000-04) Gürel, Levent; Uğur, O.
Techniques to improve the accuracy of the finite-difference time-domain (FDTD) solutions employing sinusoidal excitations are developed. The FDTD computational domain is considered as a sampled system and analyzed with respect to the aliasing error using the Nyquist sampling theorem. After a careful examination of how the high-frequency components in the excitation cause sinusoidal steady-state errors in the FDTD solutions, the use of smoothing windows and digital low-pass filters is suggested to reduce the error. The reduction in the error is demonstrated for various cases.
Open Access
Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations
(SPIE - International Society for Optical Engineering, 2004) Onural, L.
The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms. This function has interesting properties and Fourier transform relations. For example, the Fourier transform of the sampled chirp is also a sampled chirp for some sampling rates. These properties are essential in interpreting the aliasing and its effects as a consequence of sampling of the quadratic phase function, and lead to interesting and efficient algorithms to simulate Fresnel diffraction. For example, it is possible to construct discrete Fourier transform (DFT)-based algorithms to compute exact continuous Fresnel diffraction patterns of continuous, not necessarily, periodic masks at some specific distances. © 2004 Society of Photo-Optical Instrumentation Engineers.
Open Access
Synthetic TEC mapping with ordinary and universal kriging
(IEEE, 2007-06) Sayın, I.; Arıkan, F.; Arıkan, Orhan
Spatiotemporal variations in the ionosphere affects the HF and satellite communications and navigation systems. Total Electron Content (TEC) is an important parameter since it can be used to analyze the spatial and temporal variability of the ionosphere. In this study, the performance of the two widely used Kriging algorithms, namely Ordinary Kriging (OrK) and Universal Kriging (UnK), is compared over the synthetic data set. In order to represent various ionospheric states, such as quiet and disturbed days, spatially correlated residual synthetic TEC data with different variances is generated and added to trend functions. Synthetic data sampled with various type of sampling patterns and for a wide range of sampling point numbers. It is observed that for small sampling numbers and with higher variability, OrK gives smaller errors. As the sample number increases, UnK errors decrease faster. For smaller variances in the synthetic surfaces, UnK gives better results. For increasing variance and decreasing range values, usually, the errors increase for both OrK and UnK. © 2007 IEEE.