Browsing by Author "Özaktaş, Haldun M."
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Convolution and filtering in fractional fourier domains
Özaktaş, Haldun M.; Barshan, B.; Mendlovic, D. (SpringerVerlag, 1994)Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that ... 
Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms
Özaktaş, Haldun M.; Barshan, B.; Mendlovic, D.; Onural, L. (1994)A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction ... 
Costefficient approximation of linear systems with repeated and multichannel filtering configurations
Kutay, Mehmet Alper; Erden, M. F.; Özaktaş, Haldun M.; Arıkan, Orhan; Candan, Ç.; Güleryüz, Ö. (IEEE, 199805)It is possible to obtain either exact realizations or useful approximations of linear systems or matrixvector products arising in many different applications, by synthesizing them in the form of repeated or multichannel ... 
Degrees of freedom of optical systems and signals with applications to sampling and system simulation
Oktem F.S.; Özaktaş, Haldun M. (Optical Society of America, 2013)We study the degrees of freedom of optical systems and signals based on spacefrequency (phase space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the spacefrequency ... 
Design of dynamically adjustable anamorphic fractional Fourier transformer
Erden, M. F.; Özaktaş, Haldun M.; Sahin, A.; Mendlovic, D. (Elsevier BV * NorthHolland, 19970301)We form optical systems by using only free space portions and cylindrical lenses, and consider these systems as anamorphic fractional Fourier transformers. We dynamically adjust the transform order, scale factor and field ... 
Diffraction and holography from a signal processing perspective
Onural, Levent; Özaktaş, Haldun M. (SPIE, 2006)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 ... 
Diffraction field computation from arbitrarily distributed data points in space
Esmer, G. B.; Uzunov, V.; Onural, L.; Özaktaş, Haldun M.; Gotchev, A. (Elsevier BV, 200702)Computation of the diffraction field from a given set of arbitrarily distributed data points in space is an important signal processing problem arising in digital holographic 3D displays. The field arising from such ... 
Digital computation of fractional Fourier and linear canonical transforms and sparse image representation
Koc, A.; Özaktaş, Haldun M.; Bartan, B.; Gundogdu, E.; Çukur, Tolga (IEEE, 2018)Fast and accurate digital computation of the fractional Fourier transform (FRT) and linear canonical transforms (LCT) are of utmost importance in order to deploy them in real world applications and systems. The algorithms ... 
Digital computation of linear canonical transforms
Koç A.; Özaktaş, Haldun M.; Candan, C.; Kutay, M. A. (Institute of Electrical and Electronics Engineers, 2008)We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and ... 
Digital computation of the fractional Fourier transform
Özaktaş, Haldun M.; Arıkan, Orhan; Kutay, M. A.; Bozdağı, G. (Institute of Electrical and Electronics Engineers, 199609)An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with timebandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A ... 
Digital Fourier optics
Özaktaş, Haldun M.; Miller, D. A. B. (Optical Society of America, 19960310)Analog Fourier optical processing systems can perform important classes of signal processing operations in parallel, but suffer from limited accuracy. Digital–optical equivalents of such systems could be built that share ... 
The discrete fractional Fourier transform
Candan, Çağatay; Kutay, M. Alper; Özaktaş, Haldun M. (IEEE, 1999)We propose and consolidate a definition of the discrete fractional Fourier transform which generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform (FRT) generalizes ... 
The discrete fractional Fourier transform
Candan, C.; Kutay, M. A.; Özaktaş, Haldun M. (IEEE, 200005)We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the ... 
The discrete fractional Fourier transformation
Arıkan, Orhan; Kutay, M. Alper; Özaktaş, Haldun M.; Akdemir, Özer Koray (IEEE, 1996)Based on the fractional Fourier transformation of sampled periodic functions, the discrete form of the fractional Fourier transformation is obtained. It is found that only for a certain dense set of fractional orders such ... 
The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform
Barker, L.; Candan, C.; Hakioğlu, T.; Kutay, M. A.; Özaktaş, Haldun M. (Institute of Physics Publishing, 2000)Certain solutions to Harper's equation are discrete analogues of (and approximations to) the HermiteGaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and ... 
Effect of fractional Fourier transformation on timefrequency distributions belonging to the Cohen class
Özaktaş, Haldun M.; Erkaya, N.; Kutay, M. A. (Institute of Electrical and Electronics Engineers, 199602)We consider the Cohen (1989) class of timefrequency distributions, which can be obtained from the Wigner distribution by convolving it with a kernel characterizing that distribution. We show that the timefrequency ... 
Effect of sample locations on computation of the exact scalar diffraction field (in English)
Esmer, G. B.; Özaktaş, Haldun M.; Onural, Levent (IEEE, 2012)Computer generated holography is one of common methods to obtain threedimensional visualization. It can be explained by behavior of propagating waves and interference. To calculate the scalar diffraction pattern on a ... 
Effect of spatial distribution of partial information on the accurate recovery of optical wave fields
Oktem, F. S.; Özaktaş, Haldun M. (Optical Society of America, 2017)We consider the problem of recovering a signal from partial and redundant information distributed over two fractional Fourier domains. This corresponds to recovering a wave field from two planes perpendicular to the direction ... 
Elements of a hybrid interconnection theory
Özaktaş, Haldun M.; Goodman, J. W. (Optical Society of America, 19940510)We present a textbooklike treatment of hybrid systems employing both optical and electrical interconnections. We investigate how these two different interconnection media can be used in conjunction to realize a system not ... 
Energetic efficient synthesis of general mutual intensity distribution
Zalevsky, Z.; Medlovic, D.; Özaktaş, Haldun M. (Institute of Physics Publishing, 2000)The mutual intensity distribution of a light beam may contain available information. The task of encoding a given mutual intensity distribution is addressed in this paper. Various approaches for encoding the mutual intensity ...