Browsing by Author "Özdemir, A. K."

Now showing 1 - 6 of 6

Open Access
Efficient computation of joint fractional Fourier domain signal representation
(Optical Society of America, 2008) Durak, L.; Özdemir, A. K.; Arıkan, Orhan
A joint fractional domain signal representation is proposed based on an intuitive understanding from a time-frequency distribution of signals that designates the joint time and frequency energy content. The joint fractional signal representation (JFSR) of a signal is so designed that its projections onto the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR, including its relations to quadratic time-frequency representations and fractional Fourier transformations, which include the oblique projections of the JFSR. We present a fast algorithm to compute radial slices of the JFSR and the results are shown for various signals at different fractionally ordered domains.
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
Fast computation of the ambiguity function and the Wigner distribution on arbitrary line segments
(IEEE, 2001) Özdemir, A. K.; Arıkan, Orhan
By using the fractional Fourier transformation of the time-domain signals, closed-form expressions for the projections of their auto or cross ambiguity functions are derived. Based on a similar formulation for the projections of the auto and cross Wigner distributions and the well known two-dimensional (2-D) Fourier transformation relationship between the ambiguity and Wigner domains, closed-form expressions are obtained for the slices of both the Wigner distribution and the ambiguity function. By using discretization of the obtained analytical expressions, efficient algorithms are proposed to compute uniformly spaced samples of the Wigner distribution and the ambiguity function located on arbitrary line segments. With repeated use of the proposed algorithms, samples in the Wigner or ambiguity domains can be computed on non-Cartesian sampling grids, such as polar grids.
Open Access
Generalization of time-frequency signal representations to joint fractional Fourier domains
(IEEE, 2005-09) Durak, L.; Özdemir, A. K.; Arıkan, Orhan; Song, I.
The 2-D signal representations of variables rather than time and frequency have been proposed based on either Hermitian or unitary operators. As an alternative to the theoretical derivations based on operators, we propose a joint fractional domain signal representation (JFSR) based on an intuitive understanding from a time-frequency distribution constructing a 2-D function which designates the joint time and frequency content of signals. The JFSR of a signal is so designed that its projections on to the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR including its relations to quadratic time-frequency representations and fractional Fourier transformations. We present a fast algorithm to compute radial slices of the JFSR.
Open Access
Theoretical investigation on exact blind channel and input sequence estimation
(IEEE, Piscataway, NJ, United States, 1999) Özdemir, A. K.; Arıkan, Orhan
Recent work on fractionally spaced blind equalizers have shown that it is possible to exactly identify the channel and its input sequence from the noise-free channel outputs. However, the obtained results are based on a set of over-restrictive constrainst on the channel. In this paper it is shown that the exact identification can be achieved in a broader class of channels.
Open Access
Time-frequency component analyzer and its application to brain oscillatory activity
(Elsevier, 2005-06-30) Özdemir, A. K.; Karakaş S.; Çakmak, E. D.; Tüfekçi, D. İ.; Arıkan, Orhan
Currently, event-related potential (ERP) signals are analysed in the time domain (ERP technique) or in the frequency domain (Fourier analysis and variants). In techniques of time-domain and frequency-domain analysis (short-time Fourier transform, wavelet transform) assumptions concerning linearity, stationarity, and templates are made about the brain signals. In the time–frequency component analyser (TFCA), the assumption is that the signal has one or more components with non-overlapping supports in the time–frequency plane. In this study, the TFCA technique was applied to ERPs. TFCA determined and extracted the oscillatory components from the signal and, simultaneously, localized them in the time–frequency plane with high resolution and negligible cross-term contamination. The results obtained by means of TFCA were compared with those obtained by means of other commonly used techniques of ERP analysis, such as bilinear time–frequency distributions and wavelet analysis. It is suggested that TFCA may serve as an appropriate tool for capturing the localized ERP components in the time–frequency domain and for studying the intricate, frequency-based dynamics of the human brain. © 2004 Elsevier B.V. All rights reserved