The discrete fractional Fourier transform

Ankara : Department of Electrical and Electronic Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 92-96.In this work, the discrete counterpart of the continuous Fractional Fourier Transform (FrFT) is proposed, discussed and consolidated. The discrete transform generalizes the Discrete Fourier Transform (DFT) to arbitrary orders, in the same sense that the continuous FrFT generalizes the continuous time Fourier Transform. The definition proposed satisfies the requirements of unitarity, additivity of the orders and reduction to DFT. The definition proposed tends to the continuous transform as the dimension of the discrete transform matrix increases and provides a good approximation to the continuous FrFT for the finite dimensional matrices. Simulation results and some properties of the discrete FrFT are also discussed.Candan, ÇağatayM.S

An Approximate MSE Expression for Maximum Likelihood and Other Implicitly Defined Estimators of Non-Random Parameters (extended version)

An approximate mean square error (MSE) expression for the performance analysis of implicitly defined estimators of non-random parameters is proposed. An implicitly defined estimator (IDE) declares the minimizer/maximizer of a selected cost/reward function as the parameter estimate. The maximum likelihood (ML) and the least squares estimators are among the well known examples of this class. In this paper, an exact MSE expression for implicitly defined estimators with a symmetric and unimodal objective function is given. It is shown that the expression reduces to the Cramer-Rao lower bound (CRLB) and misspecified CRLB in the large sample size regime for ML and misspecified ML estimation, respectively. The expression is shown to yield the Ziv-Zakai bound (without the valley filling function) when it is used in a Bayesian setting, that is, when an a-priori distribution is assigned to the unknown parameter. In addition, extension of the suggested expression to the case of nuisance parameters is studied and some approximations are given to ease the computations for this case. Numerical results indicate that the suggested MSE expression not only predicts the estimator performance in the asymptotic region; but it is also applicable for the threshold region analysis, even for IDEs whose objective functions do not satisfy the symmetry and unimodality assumptions. Advantages of the suggested MSE expression are its conceptual simplicity and its relatively straightforward numerical calculation due to the reduction of the estimation problem to a binary hypothesis testing problem, similar to the usage of Ziv-Zakai bounds in random parameter estimation problems

Laboratuvardan Kliniğe Transplantasyon Pratiği

Transplantasyon; Temel Tıbbi Bilimler, Moleküler Tıp, Genetik ve İmmünolojiden klinik uygulamalardan destek alan multidisipliner bir tıp dalıdır. Temel bilimlerdeki başarılı çalışmaların kliniğe uygulanması, klinikte karşılaşılan sorunların da, oluşturulan deneysel hayvan modellerinde irdelenmesi, elde edilen bilgilerin klinik uygulamalara aktarılması; diğer deyişle tecrübelerin “Translational” özellikli olması günümüz transplantasyon çalışmalarında bir gerekliliktir. İmmün sistemin bileşenlerinin ve reaksiyonlarının iyi bilinmesi, hücreler arası ilişkilerde greftin reddi ya da kabul edilmesinin şartlarını doğru anlamak ve uygun laboratuvar yöntemleri ile klinik durumun aydınlatılması transplantasyonda stratejik önemdedir. Bu nedenle, klinik transplantasyon çalışmaları yapanlar temel bilimler bilgileri ile de donanımlı olmalıdırlar. Multidisipliner bir dal olma bilinci ile yapılan klinik transplantasyon çalışmalarında başarı yakalanmaktadır. Laboratuvardan Kliniğe Transplantasyon kitabımızda tüm yönleri ile transplantasyonun organizmaya etkileri ve bunların klinik sonuçlarını, çalışmalarımızın ışığında sunmayı ve tartışmayı hedefledik. Editör: Prof.Dr. Mesut İzzet TİTİZ Yardımcı Editör: Doç.Dr. Pınar AT

On The Design of Mismatched Filters With An Adjustable Matched Filtering Loss

We present a method for the design of mismatched filters minimizing the interference from unwanted targets (point target or clutter) under the constraint of matched filtering loss. The method method seeks to find the optimum filter minimizing the interference and having a desired cross-correlation with a given transmitter waveform. The method is applied to get the minimum integrated side-lobe level filters and to optimize the receivers of the pulse diversity systems

Properly Handling Complex Differentiation in Optimization and Approximation Problems

Functions of complex variables arise frequently in the formulation of signal processing problems. The basic calculus rules on differentiation and integration for functions of complex variables resemble, but are not identical to, the rules of their real variable counterparts. On the contrary, the standard calculus rules on differentiation, integration, series expansion, and so on are the special cases of the complex analysis with the restriction of the complex variable to the real line. The goal of this lecture note is to review the fundamentals of the functions of complex variables, highlight the differences and similarities with their real variable counterparts, and study the complex differentiation operation with the optimization and approximation applications in mind. More specifically, the take-home result of this lecture note is to understand the differentiation with respect to the conjugate variable (∂/∂z̅)f(z, z̅), which is known as Wirtinger calculus, and its application in optimization and approximation problem

An efficient filtering structure for Lagrange interpolation

A novel filtering structure with linear complexity is proposed for Lagrange interpolation. The structure is similar to the Farrow structure in principle, but it is more efficient and has the additional feature of being order updatable on-the-fly. The main application for the proposed structure is the implementation of fractional delay filters to mitigate the symbol synchronization errors in digital communications. Some other applications are time-delay estimation, echo cancellation, acoustic modeling, and arbitrary sampling rate conversion

An Accurate and Efficient Two-Stage Channel Estimation Method Utilizing Training Sequences with Closed Form Expressions

A novel two-stage frequency domain channel estimation method especially suitable for the estimation of long channels such as ultra wide band channels is proposed. The proposed method can efficiently use the sequences with closed form analytical expressions such as the Legendre sequences. (The suggested method does not require a computationally intense search for good training sequences which is infeasible for long training sequences.) The method is shown to present a minor improvement in the total estimation error variance when compared with the conventional single stage frequency domain channel estimation. In addition, the proposed method has a very efficient time domain implementation requiring at most 2N multiplications, where N is the training sequence length, in comparison to O(N log N) multiplications required for the conventional method

An Upper Bound on the Capacity Loss Due to Imprecise Channel State Information for General Memoryless Fading Channels

A remarkably simple upper bound on the capacity loss due to imprecise channel state information (CSI) is presented for single-input single-output (SISO) general memoryless fading channels, (Capacity Loss) ). An extension to the single-input multiple-output (SIMO) case is also provided

On the Eigenstructure of DFT Matrices

The discrete Fourier transform (DFT) not only enables fast implementation of the discrete convolution operation, which is critical for the efficient processing of analog signals through digital means, but it also represents a rich and beautiful analytical structure that is interesting on its own. A typical senior-level digital signal processing (DSP) course involves a fairly detailed treatment of DFT and a list of related topics, such as circular shift, correlation, convolution operations, and the connection of circular operations with the linear operations. Despite having detailed expositions on DFT, most DSP textbooks (including advanced ones) lack discussions on the eigenstructure of the DFT matrix. Here, we present a self-contained exposition on such