scholarly journals Multidimensional Wave Field Signal Theory: Transfer Function Relationships

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Natalie Baddour
Keyword(s):  
Transfer Function ◽  
Signal Theory ◽  
Fourier Domain ◽  
Theoretic Approach ◽  
Input Output ◽  
Coordinate Systems ◽  
Fourier Inversion ◽  
Inversion Formulas ◽  
Transmission Of Information ◽  
Physical Phenomena

The transmission of information by propagating or diffusive waves is common to many fields of engineering and physics. Such physical phenomena are governed by a Helmholtz (real wavenumber) or pseudo-Helmholtz (complex wavenumber) equation. Since these equations are linear, it would be useful to be able to use tools from signal theory in solving related problems. The aim of this paper is to derive multidimensional input/output transfer function relationships in the spatial domain for these equations in order to permit such a signal theoretic approach to problem solving. This paper presents such transfer function relationships for the spatial (not Fourier) domain within appropriate coordinate systems. It is shown that the relationships assume particularly simple and computationally useful forms once the appropriate curvilinear version of a multidimensional spatial Fourier transform is used. These results are shown for both real and complex wavenumbers. Fourier inversion of these formulas would have applications for tomographic problems in various modalities. In the case of real wavenumbers, these inversion formulas are presented in closed form, whereby an input can be calculated from a given or measured wavefield.

The uniqueness of the transfer function of linear systems from input-output observations

Metrika ◽  
1984 ◽  
Vol 31 (1) ◽  
pp. 157-181
Author(s):  
M. Deistler ◽  
B. M. Pötscher ◽  
J. Schrader
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Input Output

scholarly journals Coordinate Systems and Integration Limits for Global Flame Transfer Function Calculations

2014 ◽  
Vol 6 (4) ◽  
pp. 411-416 ◽  
Author(s):  
Luke Humphrey ◽  
Vishal Acharya ◽  
Dong-Hyuk Shin ◽  
Tim Lieuwen
Keyword(s):  
Transfer Function ◽  
Coordinate Systems

scholarly journals Contextuality: At the Borders of Paradox

2018 ◽  
Author(s):  
Samson Abramsky
Keyword(s):  
Quantum Mechanics ◽  
Theoretic Approach ◽  
Physical Phenomena

Contextuality is a key feature of quantum mechanics. We present the sheaf-theoretic approach to contextuality introduced by Abramsky and Brandenburger, and show how it covers a range of logical and physical phenomena “at the borders of paradox”.

scholarly journals Small defects reconstruction in waveguides from multifrequency one-side scattering data

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Éric Bonnetier ◽  
Angèle Niclas ◽  
Laurent Seppecher ◽  
Grégory Vial
Keyword(s):  
Born Approximation ◽  
Field Measurements ◽  
Scattering Data ◽  
Inversion Method ◽  
Local Perturbation ◽  
Fourier Domain ◽  
Fourier Inversion ◽  
Frequency Wave ◽  
Partial Data ◽  
Stable Reconstruction

<p style='text-indent:20px;'>Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work is to present a new multi-frequency inversion method to reconstruct small defects in a 2D waveguide. Given one-side multi-frequency wave field measurements of propagating modes, we use a Born approximation to provide a <inline-formula><tex-math id="M1">\begin{document}$ \text{L}^2 $\end{document}</tex-math></inline-formula>-stable reconstruction of three types of defects: a local perturbation inside the waveguide, a bending of the waveguide, and a localized defect in the geometry of the waveguide. This method is based on a mode-by-mode spacial Fourier inversion from the available partial data in the Fourier domain. Indeed, in the available data, some high and low spatial frequency information on the defect are missing. We overcome this issue using both a compact support hypothesis and a minimal smoothness hypothesis on the defects. We also provide a suitable numerical method for efficient reconstruction of such defects and we discuss its applications and limits.</p>

scholarly journals Methodology of determining of the transfer function of engagement kinematics of accelerations of an aircraft and its elliptic coordinates used for thr guidance based on time difference of arrival

2021 ◽  
pp. 12-20
Author(s):  
V. V. Legkostup ◽  
V. E. Markevich
Keyword(s):  
Transfer Function ◽  
Coordinate System ◽  
Time Difference ◽  
Coordinate Systems ◽  
Rectangular Coordinate System ◽  
Time Difference Of Arrival ◽  
Elliptic Coordinates ◽  
Curvilinear Coordinate ◽  
Aerial Vehicle ◽  
And Control

This paper discusses the problem of determining a kinematics (in terms of transfer function, as far as possible) of parameters of the motion of an aircraft expressed in the curvilinear coordinate system and control accelerations expressed in a rectangular coordinate system. Examples of curvilinear coordinate systems using in practice can be polar, biangular, two-center bipolar, elliptic, parabolic cylindrical, spherical, ellipsoidal, coordinate systems. A technique for obtaining a kinematic link for the control problem of an unmanned aerial vehicle in the elliptic coordinate system was described. It allowed to obtain simpler view of the kinematic link which could provide navigation an aircraft along the hyperbola deriving from the time difference of arrival navigation system. It can. As a result, it is possible to reduce the number of the navigation radio beacons.

Sign in / Sign up

Export Citation Format

Share Document