Browsing by Subject "Mathematical transformations"

Now showing 1 - 20 of 27

Open Access
Canonical-covariant Wigner function in polar form
(OSA - The Optical Society, 2000) Hakioǧlu, T.
The two-dimensional Wigner function was investigated in polar canonical coordinates. The covariance properties under the action of affine canonical transformations were derived. The polar canonical phase-space representations were considered important for paraxial optical systems as well as other systems in which a rotational symmetry around a particular axis was present.
Open Access
Comparative study of acceleration techniques for integrals and series in electromagnetic problems
(IEEE, 1995-06) Kinayman, Noyan; Aksun, M. I.
Most of the electromagnetic problems can be reduced down to either integrating oscillatory integrals or summing up complex series. However, limits of the integrals and the series usually extend to infinity. In addition, they may be slowly convergent. Therefore, numerically efficient techniques for evaluating the integrals or for calculating the sum of infinite series have to be used to make the numerical solution feasible and attractive. In the literature, there are a wide range of applications of such methods to various EM problems. In this paper, our main aim is to critically examine the popular series transformation (acceleration) methods which are used in electromagnetic problems and compare them by numerical examples.
Open Access
Computer vision based method for real-time fire and flame detection
(Elsevier BV, 2006-01-01) Töreyin, B. U.; Dedeoǧlu, Y.; Güdükbay, Uğur; Çetin, A. Enis
This paper proposes a novel method to detect fire and/or flames in real-time by processing the video data generated by an ordinary camera monitoring a scene. In addition to ordinary motion and color clues, flame and fire flicker is detected by analyzing the video in the wavelet domain. Quasi-periodic behavior in flame boundaries is detected by performing temporal wavelet transform. Color variations in flame regions are detected by computing the spatial wavelet transform of moving fire-colored regions. Another clue used in the fire detection algorithm is the irregularity of the boundary of the fire-colored region. All of the above clues are combined to reach a final decision. Experimental results show that the proposed method is very successful in detecting fire and/or flames. In addition, it drastically reduces the false alarms issued to ordinary fire-colored moving objects as compared to the methods using only motion and color clues. © 2005 Elsevier B.V. All rights reserved.
Open Access
Derivation of Closed-Form Green’s Functions for a General Microstrip Geometry
(1992) Aksun, M.I.; Mittra, R.
The derivation of the closed-form spatial domain Green’s functions for the vector and scalar potentials is presented for a microstrip geometry with a substrate and a super-state, whose thicknesses can be arbitrary. The spatial domain Green’s functions for printed circuits are typically expressed as Sommerfeld integrals, that are inverse Hankel transform of the corresponding spectral domain Green’s functions, and are quite time-consuming to evaluate. Closed-form representations of these Green’s functions in the spatial domains can only be obtained if the integrands are approximated by a linear combination of functions that are analytically integrable. In this paper, we show we can accomplish this by approximating the spectral domain Green’s functions in terms of complex exponentials by using the least square Prony’s method. © 1992 IEEE
Open Access
Efficient computation of surface fields excited on a dielectric-coated circular cylinder
(IEEE, 2000-10) Erturk, V. B.; Rojas, R. G.
An efficient method to evaluate the surface fields excited on an electrically large dielectric-coated circular cylinder is presented. The efficiency of the method results from the circumferentially propagating representation of the Green’s function as well as its efficient numerical evaluation along a steepest descent path. The circumferentially propagating series representation of the appropriate Green’s function is obtained from its radially propagating counterpart via Watson’s transformation and then the path of integration is deformed to the steepest descent path on which the integrand decays most rapidly. Numerical results are presented that indicate that the representations obtained here are very efficient and valid even for arbitrary small separations of the source and field points. This work is especially useful in the moment-method analysis of conformal microstrip antennas where the mutual coupling effects are important.
Open Access
Efficient fast hartley transform algorithms for hypercube-connected multicomputers
(IEEE, 1995) Aykanat, Cevdet; Derviş, A.
Although fast Hartley transform (FHT) provides efficient spectral analysis of real discrete signals, the literature that addresses the parallelization of FHT is extremely rare. FHT is a real transformation and does not necessitate any complex arithmetics. On the other hand, FHT algorithm has an irregular computational structure which makes efficient parallelization harder. In this paper, we propose a efficient restructuring for the sequential FHT algorithm which brings regularity and symmetry to the computational structure of the FHT. Then, we propose an efficient parallel FHT algorithm for medium-to-coarse grain hypercube multicomputers by introducing a dynamic mapping scheme for the restructured FHT. The proposed parallel algorithm achieves perfect load-balance, minimizes both the number and volume of concurrent communications, allows only nearest-neighbor communications and achieves in-place computation and communication. The proposed algorithm is implemented on a 32-node iPSC/21 hypercube multicomputer. High-efficiency values are obtained even for small size FHT problems. © 1995 IEEE
Open Access
Efficient use of closed-form Green's functions for three-dimensional problems involving multilayered media
(IEEE, 1994-06) Aksun, M. Irsadi; Mittra, R.
With the use of casting the spatial domain Green's functions into closed forms approach, it was demonstrated that the computational efficiency of the method of moments (MoM) for the solution of the mixed potential integral equations can be improved significantly for planar microstrip geometries. However, this approach is not effective in the improvement in the computational efficiency achieved for three-dimensional geometries in planar layered media. In this paper, discussed are the difficulties involved in using the spatial domain, closed-form Green's functions in the Method of Moments formulation for three-dimensional geometries and proposed a technique to improve the computational efficiency of the MoM.
Open Access
Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product
(Optical Society of America, 2010-07-30) Oktem, F. S.; Özaktaş, Haldun M.
Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.
Open Access
Fast and accurate algorithm for the computation of complex linear canonical transforms
(Optical Society of America, 2010-08-05) Koç A.; Özaktaş, Haldun M.; Hesselink, L.
A fast and accurate algorithm is developed for the numerical computation of the family of complex linear canonical transforms (CLCTs), which represent the input-output relationship of complex quadratic-phase systems. Allowing the linear canonical transform parameters to be complex numbers makes it possible to represent paraxial optical systems that involve complex parameters. These include lossy systems such as Gaussian apertures, Gaussian ducts, or complex graded-index media, as well as lossless thin lenses and sections of free space and any arbitrary combinations of them. Complex-ordered fractional Fourier transforms (CFRTs) are a special case of CLCTs, and therefore a fast and accurate algorithm to compute CFRTs is included as a special case of the presented algorithm. The algorithm is based on decomposition of an arbitrary CLCT matrix into real and complex chirp multiplications and Fourier transforms. The samples of the output are obtained from the samples of the input in ∼N log N time, where N is the number of input samples. A space-bandwidth product tracking formalism is developed to ensure that the number of samples is information-theoretically sufficient to reconstruct the continuous transform, but not unnecessarily redundant.
Open Access
Fast and accurate algorithms for quadratic phase integrals in optics and signal processing
(SPIE, 2011) Koç, A.; Özaktaş, Haldun M.; Hesselink L.
The class of two-dimensional non-separable linear canonical transforms is the most general family of linear canonical transforms, which are important in both signal/image processing and optics. Application areas include noise filtering, image encryption, design and analysis of ABCD systems, etc. To facilitate these applications, one need to obtain a digital computation method and a fast algorithm to calculate the input-output relationships of these transforms. We derive an algorithm of NlogN time, N being the space-bandwidth product. The algorithm controls the space-bandwidth products, to achieve information theoretically sufficient, but not redundant, sampling required for the reconstruction of the underlying continuous functions. © 2011 SPIE.
Open Access
Fast and accurate linear canonical transform algorithms
(IEEE, 2015) Özaktaş, Haldun M.; Koç, A.
Linear canonical transforms are encountered in many areas of science and engineering. Important transformations such as the fractional Fourier transform and the ordinary Fourier transform are special cases of this transform family. This family of transforms is especially important for the modelling of wave propagation. It has many applications such as noise removal, image encryption, and analysis of optical systems. Here we discuss algorithms for fast and accurate computation of these transforms. These algorithms can achieve the same accuracy and speed as fast Fourier transform algorithms, so that they can be viewed as optimal algorithms. Efficient sampling of signals plays an important part in the development of these algorithms.
Open Access
An inventory problem with two randomly available suppliers
(Institute for Operations Research and the Management Sciences, 1997) Gürler, Ü.; Parlar, M.
This paper considers a stochastic inventory model in which supply availability is subject to random fluctuations that may arise due to machine breakdowns, strikes, embargoes, etc. It is assumed that the inventory manager deals with two suppliers who may be either individually ON (available) or OFF (unavailable). Each supplier's availability is modeled as a semi-Markov (alternating renewal) process. We assume that the durations of the ON periods for the two suppliers are distributed as Erlang random variables. The OFF periods for each supplier have a general distribution. In analogy with queuing notation, we call this an Es1[Es2]/G1[G2] system. Since the resulting stochastic process is non-Markovian, we employ the "method of stages" to transform the process into a Markovian one, albeit at the cost of enlarging the state space. We identify the regenerative cycles of the inventory level process and use the renewal reward theorem to form the long-run average cost objective function. Finite time transition functions for the semi-Markov process are computed numerically using a direct method of solving a system of integral equations representing these functions. A detailed numerical example is presented for the E2[E2]/M[M] case. Analytic solutions are obtained for the particular case of "large" (asymptotic) order quantity, in which case the objective function assumes a very simple form that can be used to analyze the optimality conditions. The paper concludes with the discussion of an alternative inventory policy for modeling the random supply availability problem.
Open Access
Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems
(IEEE, 2014) Özaktaş, Haldun M.; Öktem, F. S.
We study the degrees of freedom of optical systems and signals based on space-frequency (phase-space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency plane. Based on this relationship, we discuss how to explicitly quantify the degrees of freedom of first-order optical systems with multiple apertures, and give conditions for lossless transfer. Moreover, we focus on the degrees of freedom of signals in relation to the space-frequency support and provide a sub-Nyquist sampling approach to represent signals with arbitrary space-frequency support. Implications for simulating optical systems are also discussed.
Open Access
Model based anticontrol of chaos
(IEEE, 2003) Morgül, Ömer
We will consider model based anticontrol of chaotic systems. We consider both continuous and discrete time cases. We first assume that the systems to be controlled are linear and time invariant. Under controllability assumption, we transform these systems into some canonical forms. We assume the existence of chaotic systems which has similar forms. Then by using appropriate inputs, we match the dynamics of the systems to be controlled and the model chaotic systems.
Open Access
A model-based scheme for anticontrol of some chaotic systems
(World Scientific Publishing, 2003) Morgül, Ö.
We consider a model-based approach for the anticontrol of some continuous time systems. We assume the existence of a chaotic model in an appropriate form. By using a suitable input, we match the dynamics of the controlled system and the chaotic model. We show that controllable systems can be chaotifled with the proposed method. We give a procedure to generate such chaotic models. We also apply an observer-based synchronization scheme to compute the required input.
Open Access
Motion-compensated prediction based algorithm for medical image sequence compression
(Elsevier BV, 1995-09) Oǧuz, S. H.; Gerek, Ö. N.; Çetin, A. Enis
A method for irreversible compression of medical image sequences is described. The method relies on discrete cosine transform and motion-compensated prediction to reduce intra- and inter-frame redundancies in medical image sequences. Simulation examples are presented.
Open Access
Multiple-resampling receiver design for OFDM over Doppler-distorted underwater acoustic channels
(2013) Tu, K.; Duman, T. M.; Stojanovic, M.; Proakis J. G.
In this paper, we focus on orthogonal frequency-division multiplexing (OFDM) receiver designs for underwater acoustic (UWA) channels with user-and/or path-specific Doppler scaling distortions. The scenario is motivated by the cooperative communications framework, where distributed transmitter/receiver pairs may experience significantly different Doppler distortions, as well as by the single-user scenarios, where distinct Doppler scaling factors may exist among different propagation paths. The conventional approach of front-end resampling that corrects for common Doppler scaling may not be appropriate in such scenarios, rendering a post-fast-Fourier-transform (FFT) signal that is contaminated by user-and/or path-specific intercarrier interference. To counteract this problem, we propose a family of front-end receiver structures that utilize multiple-resampling (MR) branches, each matched to the Doppler scaling factor of a particular user and/or path. Following resampling, FFT modules transform the Doppler-compensated signals into the frequency domain for further processing through linear or nonlinear detection schemes. As part of the overall receiver structure, a gradient-descent approach is also proposed to refine the channel estimates obtained by standard sparse channel estimators. The effectiveness and robustness of the proposed receivers are demonstrated via simulations, as well as emulations based on real data collected during the 2010 Mobile Acoustic Communications Experiment (MACE10, Martha's Vineyard, MA) and the 2008 Kauai Acomms MURI (KAM08, Kauai, HI) experiment.
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
Non-local, non-commutative picture in quantum mechanics and distinguished continuous canonical maps
(IOP Science, 2002) Hakioglu, T.
It is shown that continuous classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate h-independent quantum nonlinear canonical maps. It is also shown that such maps act in the non-commutative phase space under the classical covariance. A crucial result of the work is that under the action of Poisson maps a local quantum mechanical picture is converted onto a non-local picture which is then represented in a non-local Hilbert space. On the other hand, it is known that a non-local picture is equivalent by the Weyl map to a non-commutative picture which, in the context of this work, corresponds to a phase space formulation of the theory. As a result of this equivalence, a phase space Schrödinger picture can be formulated. In particular, we obtain the *-genvalue equation of Fairlie [Proc. Camb. Phil. Soc., 60, 581 (1964)] and Curtright, Fairlie and Zachos [Phys. Rev., D 58, 025002 (1998)]. In a non-local picture entanglement becomes a crucial concept. The connection between the entanglement and non-locality is explored in the context of Poisson maps and specific examples of the generation of entanglement from a local wavefunction are provided by using the concept of generalized Bell states. The results obtained are also relevant for the non-commutative soliton picture in the non-commutative field theories. We elaborate on this in the context of the scalar non-commutative field theory.
Open Access
Optimal short-time Fourier transform for monocomponent signals
(IEEE, 2004) Güven, Hüseyin Emre
New methods of improving the short-time Fourier transform representation of signals have recently emerged. These methods use linear canonical transforms to bring the signal into a minimal time-bandwidth product form. Here we show that linear canonical transforms are not sufficient to achieve the minimum time-bandwidth product for high-order modulated mono-component signals. Therefore we propose a novel short-time Fourier transform method which requires an adaptive window, making use of an initial instantaneous frequency estimator. The new approach is able to achieve the highest possible resolution for monocomponent signals. Finally, we discuss the benefits of the proposed method.