Fourier type basic systems in L2(0, σ)

1993 ◽  
pp. 83-94
Author(s):  
Mkhitar M. Djrbashian
Keyword(s):  
Fourier Type

scholarly journals Occlusion Culling for Wide-Angle Computer-Generated Holograms Using Phase Added Stereogram Technique

Photonics ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 298
Author(s):  
Juan Martinez-Carranza ◽  
Tomasz Kozacki ◽  
Rafał Kukołowicz ◽  
Maksymilian Chlipala ◽  
Moncy Sajeev Idicula
Keyword(s):  
Point Sources ◽  
Wide Angle ◽  
Computer Generated Holograms ◽  
Propagation Methods ◽  
Propagation Technique ◽  
3D Scene ◽  
Occlusion Culling ◽  
Fourier Type ◽  
Cloud Of Points

A computer-generated hologram (CGH) allows synthetizing view of 3D scene of real or virtual objects. Additionally, CGH with wide-angle view offers the possibility of having a 3D experience for large objects. An important feature to consider in the calculation of CGHs is occlusion between surfaces because it provides correct perception of encoded 3D scenes. Although there is a vast family of occlusion culling algorithms, none of these, at the best of our knowledge, consider occlusion when calculating CGHs with wide-angle view. For that reason, in this work we propose an occlusion culling algorithm for wide-angle CGHs that uses the Fourier-type phase added stereogram (PAS). It is shown that segmentation properties of the PAS can be used for setting efficient conditions for occlusion culling of hidden areas. The method is efficient because it enables processing of dense cloud of points. The investigated case has 24 million of point sources. Moreover, quality of the occluded wide-angle CGHs is tested by two propagation methods. The first propagation technique quantifies quality of point reproduction of calculated CGH, while the second method enables the quality assessment of the occlusion culling operation over an object of complex shape. Finally, the applicability of proposed occlusion PAS algorithm is tested by synthetizing wide-angle CGHs that are numerically and optically reconstructed.

Field Transforms for Multilayered Cylindrical and Spherical Structures of Finite Conductivity

1975 ◽  
Vol 53 (11) ◽  
pp. 1078-1087 ◽  
Author(s):  
E. Bahar
Keyword(s):  
Radius Of Curvature ◽  
Finite Conductivity ◽  
Electromagnetic Propagation ◽  
Wave Guides ◽  
Spherical Structures ◽  
Fourier Type ◽  
The Relationship ◽  
Conducting Cylinders ◽  
Dielectric Structures ◽  
Watson Transform

Problems of propagation around multilayered cylindrical or spherical structures possessing highly conducting cores have been analyzed in terms of discrete sets of modes. However, when propagation through the core of the structure is significant and of particular interest, the discrete set of modes is not suitable for the complete expansion of the electromagnetic fields.To provide a suitable basis for the expansion of the electromagnetic field in nonuniform multilayered, cylindrical or spheroidal, dielectric structures we derive expressions for the electric and magnetic field transforms consisting of both a discrete and a continuous spectrum of waves. The relationship between these transforms, the Kontorowich–Lebedev transform, and the discrete Watson transform is discussed. When the radius of curvature of the structure is infinite these transforms merge with generalized Fourier type transforms.The transforms can be used to investigate electromagnetic propagation through irregularly shaped dielectric wave guides, and through irregularly shaped spheroids. It can also be used to solve the problem of propagation in the interior (concave side) of irregularly shaped conducting cylinders or spheroids.

scholarly journals Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1160 ◽  
Author(s):  
Sakhi Zaman ◽  
Irshad Hussain ◽  
Dhananjay Singh
Keyword(s):  
Collocation Method ◽  
Stationary Point ◽  
Numerical Evaluation ◽  
Oscillatory Integrals ◽  
Test Problems ◽  
Fast Computation ◽  
Splitting Algorithm ◽  
Highly Oscillatory ◽  
Highly Oscillatory Integrals ◽  
Fourier Type

An adaptive splitting algorithm was implemented for numerical evaluation of Fourier-type highly oscillatory integrals involving stationary point. Accordingly, a modified Levin collocation method was coupled with multi-resolution quadratures in order to tackle the stationary point and irregular oscillations of the integrand caused by ω . Some test problems are included to verify the accuracy of the proposed methods.

Directionally Independent Failure Prediction of End-Milling Tools by Tracking Increasing Chaotic Noise at the Machining Frequencies Due to Wear

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Christopher A. Suprock ◽  
John T. Roth
Keyword(s):  
Discrete Cosine Transform ◽  
End Milling ◽  
Dimensional Space ◽  
Data Sets ◽  
Cosine Transform ◽  
Modal Reduction ◽  
Milling Operations ◽  
Higher Dimensional ◽  
System Energy ◽  
Fourier Type

Accurate on-line forecasting of a tool’s condition during end-milling operations is advantageous to the functionality and reliability of automated industrial processes. The ability to disengage the tool prior to catastrophic failure reduces manufacturing costs, excessive machine deterioration, and personnel hazards. Rapid computational feedback describing the system’s state is critical for realizing a practical failure forecasting model. To this end, spectral analysis by fast Fourier type algorithms allows a rapid computational response. The research described herein explores the development of nontraditional real fast Fourier transform (discrete cosine transform) based algorithms performed in unique higher-dimensional states of observed data sets. Moreover, the developed Fourier algorithm quantifies chaotic noise rather than relying on the more traditional observation of system energy. By increasing the vector dimensionality of the discrete cosine transform, the respective linear transform basis more effectively cross correlates the transform data into fewer (more significant) transform coefficients. Thus, a single vector in orthogonally higher-dimensional space is observed instead of multiple orthogonal vectors in single-dimensional space. More specifically, a novel modal reduction technique is utilized to track trends measured from triaxial force dynamometer signals. This transformation effectively achieves both modal reduction and directional independence by observing the chaotic noise instead of system energy. Algorithm output trends from six end-milling life tests are tracked from both linear and pocketing maneuvers in order to demonstrate the technique’s capabilities. In all six tests, the algorithm predicts impending tool failure with sufficient time for tool removal.

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