Browsing by Subject "Linear transformations"
Now showing 1 - 4 of 4
Results Per Page
Sort Options
Item Open Access Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems(IEEE, 2014) Özaktaş, Haldun M.; Öktem, F. S.We study the degrees of freedom of optical systems and signals based on space-frequency (phase-space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency plane. Based on this relationship, we discuss how to explicitly quantify the degrees of freedom of first-order optical systems with multiple apertures, and give conditions for lossless transfer. Moreover, we focus on the degrees of freedom of signals in relation to the space-frequency support and provide a sub-Nyquist sampling approach to represent signals with arbitrary space-frequency support. Implications for simulating optical systems are also discussed.Item Open Access Parametric identification of Hybrid Linear-Time-Periodic Systems(Elsevier B.V., 2016) Uyanık, İ.; Saranlı U.; Morgϋl, Ö.; Ankaralı, M. M.In this paper, we present a state-space system identification technique for a class of hybrid LTP systems, formulated in the frequency domain based on input-output data. Other than a few notable exceptions, the majority of studies in the state-space system identification literature (e.g. subspace methods) focus only on LTI systems. Our goal in this study is to develop a technique for estimating time-periodic system and input matrices for a hybrid LTP system, assuming that full state measurements are available. To this end, we formulate our problem in a linear regression framework using Fourier transformations, and estimate Fourier series coefficients of the time-periodic system and input matrices using a least-squares solution. We illustrate the estimation accuracy of our method for LTP system dynamics using a hybrid damped Mathieu function as an example. © 2016Item Open Access Quantum canonical transformations in star-product formalism(IOP, 2013) Dereli, T.; Hakioğlu, Tuğrul; Temen, A.We study construction of the star-product version of three basic quantum canonical transformations which are known as the generators of the full canonical algebra. By considering the fact that star-product of c-number phase-space functions is in complete isomorphism to Hilbert-space operator algebra, it is shown that while the constructions of gauge and point transformations are immediate, generator of the interchanging transformation deforms this isomorphism. As an alternative approach, we study all of them within the deformed form. How to transform any c-number function under linear-nonlinear transformations and the intertwining method are shown within this argument as the complementary subjects of the text.Item Open Access Sparsity Based Image Retrieval using relevance feedback(IEEE, 2012) Günay, Osman; Çetin, A. EnisIn this paper, a Content Based Image Retrieval (CBIR) algorithm employing relevance feedback is developed. After each round of user feedback Biased Discriminant Analysis (BDA) is utilized to find a transformation that best separates the positive samples from negative samples. The algorithm determines a sparse set of eigenvectors by L1 based optimization of the generalized eigenvalue problem arising in BDA for each feedback round. In this way, a transformation matrix is constructed using the sparse set of eigenvectors and a new feature space is formed by projecting the current features using the transformation matrix. Transformations developed using the sparse signal processing method provide better CBIR results and computational efficiency. Experimental results are presented. © 2012 IEEE.