Linear Algebraic Analysis of Fractional Fourier Domain Interpolation

Date

2009-01-01

Author

Öktem, Sevinç Figen

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

191
views

0
downloads

n this work, we present a novel linear algebraic approach to certain signal interpolation problems involving the fractional Fourier transform. These problems arise in wave propagation, but the proposed approach to these can also be applicable to other areas. We see this interpolation problem as the problem of determining the unknown signal values from the given samples within some tolerable error We formulate the problem as a linear system of equations and use the condition number as a measure of redundant information in given samples. By analyzing the effect of the number of known samples and their distributions on the condition number with simulation examples, we aim to investigate the redundancy and information relations between the given data

Subject Keywords

Computation, Transform

URI

https://hdl.handle.net/11511/52224

DOI

https://doi.org/10.1109/siu.2009.5136535

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Exact Solutions of Some Partial Differential Equations Using the Modified Differential Transform Method Cansu Kurt, Ümmügülsüm; Ozkan, Ozan (2018-03-01) In this paper, we present the modification of the differential transform method by using Laplace transform and Pade approximation to obtain closed form solutions of linear and nonlinear partial differential equations. Some illustrative examples are given to demonstrate the activeness of the proposed technique. The obtained results ensure that this modified method is capable of solving a large number of linear and nonlinear PDEs that have wide application in science and engineering. It solves the drawbacks i...
Digital computation of linear canonical transforms Koc, Aykut; Ozaktas, Haldun M.; Candan, Çağatay; KUTAY, M. Alper (2008-06-01) We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take similar to N...
Asymptotic behavior of linear impulsive integro-differential equations Akhmet, Marat; YILMAZ, Oğuz (Elsevier BV, 2008-08-01) Asymptotic equilibria of linear integro-differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro-differential equations are established. A new Gronwall-Bellman type lemma for integro-differential inequalities is proved. An example is given to demonstrate the validity of one of the results.
Dynamic programming for a Markov-switching jump-diffusion Azevedo, N.; Pinheiro, D.; Weber, Gerhard Wilhelm (Elsevier BV, 2014-09-01) We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial in...
Linear Canonical Domains and Degrees of Freedom of Signals and Systems Öktem, Sevinç Figen (2016-01-01) We discuss the relationships between linear canonical transform (LCT) domains, fractional Fourier transform (FRT) domains, and the space-frequency plane. In particular, we show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and monotonically ordered by the corresponding fractional order parameter and provides a more transparent view of the evolution of light through an optical system modeled...

Citation Formats

S. F. Öktem, “Linear Algebraic Analysis of Fractional Fourier Domain Interpolation,” 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52224.