Browsing by Subject "Fourier transforms"

Now showing 1 - 20 of 74

Open Access
About the Wigner distribution of a graded index medium and the fractional fourier transform operation
(SPIE, 1993-08) Özaktaş, Haldun M.; Mendlovic, D.; Lohmann, A. W.
Upon propagation through quadratic graded index media, the Wigner distribution of the wavefunction of light rotates uniformly. As a consequence, a definition of fractional Fourier transforms based on rotating the functions Wigner distribution, and another based on propagation through graded index media, are equivalent.
Open Access
Autofocus method in thermal cameras based on image histogram
(IEEE, 2011) Turgay, E.; Teke, Oğuzhan
In this paper, a new histogram based auto-focusing method for thermal cameras is proposed. This proposed method is realized by FPGA (Field Programmable Gate Array) and DSP (Digital Signal Processor) working together and simultaneously. HF (High Frequency) component, obtained from real-time image flow by FPGA and DSP is used for auto-focusing process. Proposed method is able to determine the focus direction from the HF component produced in the process of histogram equalization by FPGA, unlike Fourier transform and pixel differenve based methods in the literature. With this superiority, proposed method requires no extra calculation for thermal cameras for which histogram equalization is necessary. Analysis show that proposed method is successful on the simulations and scanning thermal cameras.
Open Access
Chirp filtering in the fractional Fourier domain
(Optical Society of America, 1994-11-10) Dorsch, R. G.; Lohmann, A. W.; Bitran, Y.; Mendlovic, D.; Özaktaş, Haldun M.
In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of the Wigner-distribution function by an angle connected with the FRT order. Thus with the FRT tool a chirp and a delta function can be transformed one into the other. Taking the chirp as additive noise, the FRT is used for filtering the line delta function in the appropriate fractional Fourier domain. Experimental filtering results for a Gaussian input function, which is modulated by an additive chirp noise, are shown. Excellent agreement between experiments and computer simulations is achieved.
Open Access
Compact optical temporal processors
(Optical Society of America, 1995) Mendlovic, D.; Melamed, O.; Özaktaş, Haldun M.
Optical signal processing can be done with time-lens devices. A temporal processor based on chirp-z transformers is suggested. This configuration is more compact than a conventional 4-f temporal processor. On the basis of implementation aspects of such a temporal processor, we did a performance analysis. This analysis leads to the conclusion that an ultrafast optical temporal processor can be implemented.
Open Access
Comparative analysis of different approaches to target differentiation and localization with sonar
(Elsevier, 2003) Barshan, B.; Ayrulu, B.
This study compares the performances of different methods for the differentiation and localization of commonly encountered features in indoor environments. Differentiation of such features is of interest for intelligent systems in a variety of applications such as system control based on acoustic signal detection and identification, map building, navigation, obstacle avoidance, and target tracking. Different representations of amplitude and time-of-2ight measurement patterns experimentally acquired from a real sonar system are processed. The approaches compared in this study include the target differentiation algorithm, Dempster-Shafer evidential reasoning, different kinds of voting schemes, statistical pattern recognition techniques (k-nearest neighbor classifier, kernel estimator, parameterized density estimator, linear discriminant analysis, and fuzzy c-means clustering algorithm), and artificial neural networks. The neural networks are trained with different input signal representations obtained usingpre-processing techniques such as discrete ordinary and fractional Fourier, Hartley and wavelet transforms, and Kohonen's self-organizing feature map. The use of neural networks trained with the back-propagation algorithm, usually with fractional Fourier transform or wavelet pre-processing results in near perfect differentiation, around 85% correct range estimation and around 95% correct azimuth estimation, which would be satisfactory in a wide range of applications. © 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.
Open Access
Comparison of local and global computation and its implications for the role of optical interconnections in future nanoelectronic systems
(Elsevier, 1993) Özaktaş, Haldun M.; Goodman J. W.
Various methods of simulating diffusion phenomena with parallel hardware are discussed. In particular methods are compared requiring local and global communication among the processors in terms of total computation time. Systolic convolution on a locally connected array is seen to exhibit an asymptotic advantage over Fourier methods on a globally connected array. Whereas this may translate into a numerical advantage for extremely large numbers of ultrafast devices for two-dimensional systems, this is unlikely for three-dimensional systems. Thus global Fourier methods will be advantageous for three-dimensional systems for foreseeable device speeds and system sizes. The fact that optical interconnections are potentially advantageous for implementing the longer connections of such globally connected systems suggests that they can be beneficially employed in future nanoelectronic computers. Heat removal considerations play an important role in our conclusions.
Open Access
Continuous and discrete fractional fourier domain decomposition
(IEEE, 2000) Yetik, İ. Şamil; Kutay, M. A.; Özaktaş, H.; Özaktaş, Haldun M.
We introduce the fractional Fourier domain decomposition for continuous and discrete signals and systems. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems.
Open Access
Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations
(IEEE, 1998-05) Kutay, Mehmet Alper; Erden, M. F.; Özaktaş, Haldun M.; Arıkan, Orhan; Candan, Ç.; Güleryüz, Ö.
It is possible to obtain either exact realizations or useful approximations of linear systems or matrix-vector products arising in many different applications, by synthesizing them in the form of repeated or multi-channel filtering operations in fractional Fourier domains, resulting in much more efficient implementations with acceptable decreases in accuracy. By varying the number and configuration of filter blocks, which may take the form of arbitrary flow graphs, it is possible to trade off between accuracy and efficiency in the desired manner. The proposed scheme constitutes a systematic way of exploiting the information inherent in the regularity or structure of a given linear system or matrix, even when that structure is not readily apparent.
Open Access
Design of dynamically adjustable anamorphic fractional Fourier transformer
(Elsevier BV * North-Holland, 1997-03-01) Erden, M. F.; Özaktaş, Haldun M.; Sahin, A.; Mendlovic, D.
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 curvature of both orthogonal dimensions of anamorphic fractional Fourier transformation by just changing the focal lengths of cylindrical lenses used in the proposed setups. Here, we also consider two approaches for implementing cylindrical lenses with dynamically adjustable focal lengths. There may also be some other methods to obtain cylindrical lenses having adjustable focal lengths which can successfully be used in these proposed setups.
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
Diffraction from a wavelet point of view
(Optical Society of America, 1993-06-01) Onural, L.
The system impulse response representing the Fresnel diffraction is shown to form a wavelet family of functions. The scale parameter of the wavelet family represents the depth (distance). This observation relates the diffraction-holography-related studies and the wavelet theory. The results may be used in various optical applications such as designing robust volume optical elements for optical signal processing and finding new formulations for optical inverse problems. The results also extend the wavelet concept to the nonbandpass family of functions with the implication of new applications in signal processing. The presented wavelet structure, for example, is a tool for space-depth analysis.
Open Access
Digital computation of the fractional Fourier transform
(Institute of Electrical and Electronics Engineers, 1996-09) Özaktaş, Haldun M.; Arıkan, Orhan; Kutay, M. A.; Bozdağı, G.
An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed.
Open Access
The discrete fractional Fourier transform
(IEEE, 1999) Candan, Çağatay; Kutay, M. Alper; Özaktaş, Haldun M.
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 continuous ordinary Fourier Transform. This definition is based on a particular set of eigenvectors of the DFF which constitutes the discrete counterpart of the set of Hermite-Gaussian functions. The fact that this definition satisfies all the desirable properties expected of the discrete FRT, supports our confidence that it will be accepted as the definitive definition of this transform.
Open Access
The discrete fractional Fourier transformation
(IEEE, 1996) Arıkan, Orhan; Kutay, M. Alper; Özaktaş, Haldun M.; Akdemir, Özer Koray
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 a discrete transformation is possible to define. Also, for its efficient computation a fast algorithm, which has the same complexity as the FFT, is given.
Open Access
Durağan olmayan çok bileşenli boğucu sinyaller için yeni bir uyarlanır karışma çıkarıcı analizi
(IEEE, 2005) Durak, L.; Arıkan, Orhan; Song, I.
A novel adaptive short-time Fourier transform (STFT) implementation for the analysis of non-stationary multi-component jammer signals is introduced. The proposed time-frequency distribution is the fusion of optimum STFTs of individual signal components that are based on the recently introduced generalized time-bandwidth product (GTBP) definition. The GTBP optimal STFTs of the components are combined through thresholding and obtaining the individual component support images, which are related with the corresponding GTBP optimal STFTs.
Open Access
Effect of fractional Fourier transformation on time-frequency distributions belonging to the Cohen class
(Institute of Electrical and Electronics Engineers, 1996-02) Özaktaş, Haldun M.; Erkaya, N.; Kutay, M. A.
We consider the Cohen (1989) class of time-frequency distributions, which can be obtained from the Wigner distribution by convolving it with a kernel characterizing that distribution. We show that the time-frequency distribution of the fractional Fourier transform of a function is a rotated version of the distribution of the original function, if the kernel is rotationally symmetric. Thus, the fractional Fourier transform corresponds to rotation of a relatively large class of time-frequency representations (phase-space representations), confirming the important role this transform plays in the study of such representations.
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
An efficient method for electromagnetic characterization of 2-D geometries in stratified media
(IEEE, 2002) Aksun, M. I.; Çalışkan, F.; Gürel, Levent
A numerically efficient technique, based on the spectral-domain method of moments (MoM) in conjunction with the generalized pencil-of-functions (GPOF) method, is developed for the characterization of two-dimensional geometries in multilayer planar media. This approach provides an analytic expression for all the entries of the MoM matrix, explicitly including the indexes of the basis and testing functions provided that the Galerkin's MoM is employed. This feature facilitates an efficient modification of the geometry without the necessity of recalculating the additional elements in the MoM matrix. To assess the efficiency of the approach, the results and the matrix fill times are compared to those obtained with two other efficient methods, namely, the spatial-domain MoM in conjunction with the closed-form Green's functions, and a fast Fourier transform algorithm to evaluate the MoM matrix entries. Among these, the spectral-domain MoM using the GPOF algorithm is the most efficient approach for printed multilayer geometries.
Open Access
Energetic efficient synthesis of general mutual intensity distribution
(Institute of Physics Publishing, 2000) Zalevsky, Z.; Medlovic, D.; Özaktaş, Haldun M.
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 function have been previously proposed. However, all of them provide low energetic efficiency and commonly require sophisticated production methods. The idea of using a phase-only filter for performing this synthesis is hereby investigated. The proposed method is numerically examined for the case of placing the mutual intensity generating filter in the fractional Fourier domain.
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.