Browsing by Author "Durak, L."
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Item 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.Item Open Access Efficient computation of joint fractional Fourier domain signal representation(Optical Society of America, 2008) Durak, L.; Özdemir, A. K.; Arıkan, OrhanA 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.Item 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.Item Open Access A novel STFT implementation for the analysis of non-stationary jammer interference(IASTED, 2004) 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.Item Open Access Short-time Fourier transform: two fundamental properties and an optimal implementation(IEEE, 2003) Durak, L.; Arıkan, OrhanShift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with the Hermite-Gaussian kernels satisfies both the shift invariance and rotation invariance properties that are satisfied by the Wigner distribution (WD). By extending the time-bandwidth product (TBP) concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is defined. For mono-component signals, it is shown that GTBP provides a rotation independent measure of compactness. Similar to the TBP optimal STFT, the GTBP optimal STFT that causes the least amount of increase in the GTBP of the signal is obtained. Finally, a linear canonical decomposition of the obtained GTBP optimal STFT analysis is presented to identify its relation to the rotationally invariant STFT.