Browsing by Subject "Discrete Fourier transforms"

Now showing 1 - 9 of 9

Open Access
Analysis of an arbitrary-profile, cylindrical, impedance reflector surface illuminated by an E-polarized complex line source beam
(VSP BV, 2014) Kuyucuoglu, F.; Oǧuzer, T.; Avgin, I.; Altintas, A.
Electromagnetic scattering from a cylindrical reflector surface having an arbitrary conic section profile is studied. We assumed an electrically thin layer antenna illuminated by a complex line source in E-polarization mode. Our boundary value formulation, without loss of generality, involves an integral equation approach having impedance-type thin-layer boundary conditions. For simplicity, we also considered both faces of the reflector of the same uniform impedance value. Our computation employs the Method of Analytical Regularization (MAR) technique: the integral equations are converted into the discrete Fourier transform domain yielding two coupled dual series equations, which are then solved by the Fourier inversion and Riemann Hilbert Problem techniques. We demonstrate the accuracy and the convergence behaviors of our numerically solved MAR results that can serve as an accurate benchmark for comparison with widely used results obtained by approximate boundary conditions. © 2013 Taylor and Francis.
Open Access
Applications of hybrid discrete Fourier transform moment method to the fast analysis of large rectangular dipole arrays printed on a thin grounded dielectric substrate
(Wiley, 2002) Chou, H.-T.; Ho, H.-K.; Civi, O. A.; Erturk, V. B.
Recently a discrete Fourier transform-method of moments (DFT-MoM) scheme was developed for fast analysis of electrically large rectangular planar dipole arrays, which has been shown to be very efficient in terms of number reduction of unknown variables and computational complexity. The applications of this DFT-MoM to treat dipole arrays printed on a grounded dielectric substrate are examined in this Letter. Numerical results are presented to validate its efficiency and accuracy.
Open Access
Average error in recovery of sparse signals and discrete fourier transform
(IEEE, 2012-04) Özçelikkale, Ayça; Yüksel, S.; Özaktaş Haldun M.
In compressive sensing framework it has been shown that a sparse signal can be successfully recovered from a few random measurements. The Discrete Fourier Transform (DFT) is one of the transforms that provide the best performance guarantees regardless of which components of the signal are nonzero. This result is based on the performance criterion of signal recovery with high probability. Whether the DFT is the optimum transform under average error criterion, instead of high probability criterion, has not been investigated. Here we consider this optimization problem. For this purpose, we model the signal as a random process, and propose a model where the covariance matrix of the signal is used as a measure of sparsity. We show that the DFT is, in general, not optimal despite numerous results that suggest otherwise. © 2012 IEEE.
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
Efficient analysis of large phased arrays using iterative MoM with DFT-based acceleration algorithm
(John Wiley & Sons, Inc., 2003) Ertürk, V. B.; Chou, H-T.
A discrete Fourier transform (DFT)-based iterative method of moments (IMoM) algorithm is developed to provide an O(Ntot) computational complexity and memory storages for the efficient analysis of electromagnetic radiation/scattering from large phased arrays. Here, Ntot is the total number of unknowns. Numerical results for both printed and free-standing dipole arrays are presented to validate the algorithm's efficiency and accuracy.
Open Access
Fall detection using single-tree complex wavelet transform
(Elsevier, 2013) Yazar, A.; Keskin, F.; Töreyin, B. U.; Çetin, A. Enis
The goal of Ambient Assisted Living (AAL) research is to improve the quality of life of the elderly and handicapped people and help them maintain an independent lifestyle with the use of sensors, signal processing and telecommunications infrastructure. Unusual human activity detection such as fall detection has important applications. In this paper, a fall detection algorithm for a low cost AAL system using vibration and passive infrared (PIR) sensors is proposed. The single-tree complex wavelet transform (ST-CWT) is used for feature extraction from vibration sensor signal. The proposed feature extraction scheme is compared to discrete Fourier transform and mel-frequency cepstrum coefficients based feature extraction methods. Vibration signal features are classified into "fall" and "ordinary activity" classes using Euclidean distance, Mahalanobis distance, and support vector machine (SVM) classifiers, and they are compared to each other. The PIR sensor is used for the detection of a moving person in a region of interest. The proposed system works in real-time on a standard personal computer.
Open Access
Fast acceleration algorithm based on DFT expansion for the iterative MoM analysis of electromagnetic radiation/scattering from two-dimensional large phased arrays
(IEEE, 2002) Ertürk, Vakur B.; Chou, H. T.
An acceleration algorithm based on Discrete Fourier Transform (DFT) is developed to reduce the computational complexity and memory storages of iterative methods of moment (IMoM) solution to O(Ntot), where Ntot is the total number of elements in the array. As such, numerical results for free-standing dipoles obtained using IMoM-DFT approach are presented and compared with the conventional MoM solution.
Open Access
Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations
(SPIE - International Society for Optical Engineering, 2004) Onural, L.
The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms. This function has interesting properties and Fourier transform relations. For example, the Fourier transform of the sampled chirp is also a sampled chirp for some sampling rates. These properties are essential in interpreting the aliasing and its effects as a consequence of sampling of the quadratic phase function, and lead to interesting and efficient algorithms to simulate Fresnel diffraction. For example, it is possible to construct discrete Fourier transform (DFT)-based algorithms to compute exact continuous Fresnel diffraction patterns of continuous, not necessarily, periodic masks at some specific distances. © 2004 Society of Photo-Optical Instrumentation Engineers.
Open Access
Unitary precoding and basis dependency of MMSE performance for gaussian erasure channels
(IEEE, 2014) Özçelikkale, A.; Yüksel S.; Özaktaş, Haldun M.
We consider the transmission of a Gaussian vector source over a multidimensional Gaussian channel where a random or a fixed subset of the channel outputs are erased. Within the setup where the only encoding operation allowed is a linear unitary transformation on the source, we investigate the minimum mean-square error (MMSE) performance, both in average, and also in terms of guarantees that hold with high probability as a function of the system parameters. Under the performance criterion of average MMSE, necessary conditions that should be satisfied by the optimal unitary encoders are established and explicit solutions for a class of settings are presented. For random sampling of signals that have a low number of degrees of freedom, we present MMSE bounds that hold with high probability. Our results illustrate how the spread of the eigenvalue distribution and the unitary transformation contribute to these performance guarantees. The performance of the discrete Fourier transform (DFT) is also investigated. As a benchmark, we investigate the equidistant sampling of circularly wide-sense stationary signals, and present the explicit error expression that quantifies the effects of the sampling rate and the eigenvalue distribution of the covariance matrix of the signal. These findings may be useful in understanding the geometric dependence of signal uncertainty in a stochastic process. In particular, unlike information theoretic measures such as entropy, we highlight the basis dependence of uncertainty in a signal with another perspective. The unitary encoding space restriction exhibits the most and least favorable signal bases for estimation. © 2014 IEEE.