Browsing by Author "Kutay, Mehmet Alper"

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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
Generalized filtering configurations with applications in digital and optical signal and image processing
(1999) Kutay, Mehmet Alper
In this thesis, we first give a brief summary of the fractional Fourier transform which is the generalization of the ordinary Fourier transform, discuss its importance in optical and digital signal processing and its relation to time-frequency representations. We then introduce the concept of filtering circuits in fractional Fourier domains. This concept unifies the multi-stage (repeated) and multi-channel (parallel) filtering configurations which are in turn generalizations of single domain filtering in fractional Fourier domains. We show that these filtering configurations allow a cost-accuracy tradeoff by adjusting the number of stages or channels. We then consider the application of these configurations to three important problems, namely system synthesis, signal synthesis, and signal recovery, in optical and digital signal processing. In the system and signal synthesis problems, we try to synthesize a desired system characterized by its kernel, or a desired signal characterized by its second order statistics by using fractional Fourier domain filtering circuits. In the signal recovery problem, we try to recover or estimate a desired signal from its degraded version. In all of the examples we give, significant improvements in performance are obtained with respect to single domain filtering methods with only modest increases in optical or digital implementation costs. Similarly, when the proposed method is compared with the direct implementation of general linear systems, we see that significant computational savings are obtained with acceptable decreases in performance.
Open Access
Introduction to the fractional fourier transform and its applications
(Elsevier, 1999) Özaktaş, Haldun M.; Kutay, Mehmet Alper; Mendlovic, D.; Hawkes, P. W.
This chapter is an introduction to the fractional Fourier transform and its applications. The fractional Fourier transform is a generalization of the ordinary Fourier transform with an order parameter a. Mathematically, the ath order fractional Fourier transform is the ath power of the Fourier transform operator. The a = 1st order fractional transform is the ordinary Fourier transform. In essence, the ath order fractional Fourier transform interpolates between a function f(u) and its Fourier transform F(μ). The 0th order transform is simply the function itself, whereas the 1st order transform is its Fourier transform. The 0.5th transform is something in between, such that the same operation that takes us from the original function to its 0.5th transform will take us from its 0.5th transform to its ordinary Fourier transform. More generally, index additivity is satisfied: The a2th transform of the a1th transform is equal to the (a2 + a1)th transform. The –1th transform is the inverse Fourier transform, and the –ath transform is the inverse of the ath transform.
Open Access
Optical implementation of linear canonical transforms
(Springer Verlag, 2016) Kutay, Mehmet Alper; Özaktaş, Haldun M.; Rodrigo, J. A.
We consider optical implementation of arbitrary one-dimensional and two-dimensional linear canonical and fractional Fourier transforms using lenses and sections of free space. We discuss canonical decompositions, which are generalizations of common Fourier transforming setups. We also look at the implementation of linear canonical transforms based on phase-space rotators. © Springer International Publishing Switzerland 2016.
Open Access
Optical information processing: A historical overview
(Academic Press, 2021-12) Özaktaş, Haldun Memduh; Kutay, Mehmet Alper
Optical information processing lies at the intersection of optics and signal processing. It involves the processing of optical information as well as the use of optical means to process information, the later being the main emphasis of this work. A historical review of various forms of optical signal processing and holography, optoelectronic and digital optical computing, and optical interconnections is given.