Browsing by Author "Kutay, M. Alper"

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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
Enhancement of images corrupted with signal dependent noise: Application to ultrasonic imaging
(1993-11) Kutay, M. Alper; Karaman, Mustafa; Bozdağı, Gözde
An adaptive filter for smoothing images corrupted by signal dependent noise is presented. The filter is mainly developed for speckle suppression in medical B-scan ultrasonic imaging. The filter is based on mean filtering of the image using appropriately shaped and sized local kernels. Each filtering kernel, fitting to the local homogeneous region, is obtained through local statistics based region growing. Performance of the proposed scheme have been tested on a B-scan image of a standard tissue-mimicking ultrasound resolution phantom. The results indicate that the filter effectively reduces the speckle while preserving the resolvable details. The performance figures obtained through computer simulations on the phantom image are presented in a comparative way with some existing speckle iippression schemes.
Open Access
Optimal filtering in fractional Fourier domains
(IEEE, 1995) Kutay, M. Alper; Onural, Levent; Özaktaş Haldun M.; Arıkan, Orhan
The ordinary Fourier transform is suited best for analysis and processing of time-invariant signals and systems. When we are dealing with time-varying signals and systems, filtering in fractional Fourier domains might allow us to estimate signals with smaller minimum-mean-square error (MSE). We derive the optimal fractional Fourier domain filter that minimizes the MSE for given non-stationary signal and noise statistics, and time-varying distortion kernel. We present an example for which the MSE is reduced by a factor of 50 as a result of filtering in the fractional Fourier domain, as compared to filtering in the conventional Fourier or time domains. We also discuss how the fractional Fourier transformation can be computed in O(N log N) time, so that the improvement in performance is achieved with little or no increase in computational complexity.
Open Access
Solution and cost analysis of general multi-channel and multi-stage filtering circuits
(IEEE, 1998-10) Kutay, M. Alper; Arıkan, Orhan; Özaktaş, Haldun M.; Erden, M. F.; Özaktaş, Hakan
The fractional Fourier domain multi-channel and multi-stage filtering configurations that have been recently proposed enable us to obtain either exact realizations or useful approximations of linear systems or matrix-vector products in many different applications. We discuss the solution and cost analysis for these configurations. It is shown that the problem can be reduced to a least squares problem which can be solved with fast iterative techniques.