DOA Refinement Through Complex Parabolic Interpolation of a Sparse Recovered Signal

2021 ◽  
Vol 28 ◽  
pp. 274-278
Author(s):  
Luca Pallotta ◽  
Gaetano Giunta ◽  
Alfonso Farina
Keyword(s):  
Parabolic Interpolation

scholarly journals An Efficient Method for Forming Parabolic Curves and Surfaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 592
Author(s):  
Yuliy Lyachek
Keyword(s):  
Mathematical Description ◽  
Reference Points ◽  
Coordinate Systems ◽  
Parabolic Curve ◽  
Curves And Surfaces ◽  
Parabolic Interpolation ◽  
Second Derivatives ◽  
The Matrix ◽  
Positive Effect ◽  
Continuity Analysis

A new method for the formation of parabolic curves and surfaces is proposed. It does not impose restrictions on the relative positions in space of the sequence of reference points relative to each other, meaning it compares favorably with other prototypes. The disadvantages of the Overhauser and Brever–Anderson methods are noted. The method allows one to effectively form and edit curves and surfaces when changing the coordinates of any given point. This positive effect is achieved due to the appropriate choice of local coordinate systems for the mathematical description of each parabola, which together define a composite interpolation curve or surface. The paper provides a detailed mathematical description of the method of parabolic interpolation of curves and surfaces based on the use of matrix calculations. Analytical descriptions of a composite parabolic curve and its first and second derivatives are given, and continuity analysis of these factors is carried out. For the matrix of points of the defining polyhedron, expressions are presented that describe the corresponding surfaces, as well as the unit normal at any point. The comparative table of the required number of pseudo-codes for calculating the coordinates of one point for constructing a parabolic curve for the three methods is given.

Numerical Analysis and Performance Test of Interactive Platform Based on Multi-Media Internet Architecture

2014 ◽  
Vol 556-562 ◽  
pp. 5705-5709 ◽  
Author(s):  
Can Xin Wei
Keyword(s):  
Streaming Media ◽  
Loss Rate ◽  
Packet Loss Rate ◽  
Ideological And Political Education ◽  
Interpolation Algorithm ◽  
Media Technology ◽  
Newton Interpolation ◽  
Parabolic Interpolation ◽  
Teachers And Students ◽  
Streaming Media Technology

Streaming media technology is also known as streaming media technology. Users can experience playing while downloading function, which improves the transmission speed of multimedia information on the internet. In this paper, we use streaming media technology, combined with the parabolic interpolation and Newton interpolation algorithm, design multimedia interactive platform of the college students' ideological and political education and comprehensive education. The overall structure of the platform is composed of multimedia, streaming media distribution equipment, school network, clients of teachers and students. On the internet between the teachers and students, student and students they can communicate ideological and political. In order to test the performance of network, we use the iperf software to test packet loss rate and delay characteristics of the network. The results show that Newton interpolation method has better delay characteristics, parabolic interpolation algorithm has low packet loss rate. It provides technical reference for the application of multimedia technology in the ideological and political education.

Exact Interpolation of Fourier Transform Spectra

1983 ◽  
Vol 37 (2) ◽  
pp. 153-166 ◽  
Author(s):  
Carlo Giancaspro ◽  
Melvin B. Comisarow
Keyword(s):  
Fourier Transform ◽  
Graphical Form ◽  
Acquisition Time ◽  
Time Domain Signal ◽  
Parabolic Interpolation ◽  
Interpolation Procedure ◽  
True Frequency ◽  
Fourier Transform Spectra ◽  
The Time Domain ◽  
Absorption Mode

A systematic study of interpolation of Fourier transform (FT) spectra is reported. Interpolation errors are examined for both frequency determination and intensity determination for different interpolation procedures for both absorption mode and magnitude mode FT spectra. The errors are presented in both analytical and graphical form as functions of the number of zero-fillings and ( T/τ), the ratio of the acquisition time to the relaxation time of the time domain signal. For interpolation of absorption mode spectra, parabolic interpolation is superior to Lorentzian interpolation if T/τ < 2. For T/τ > 2, Lorentzian interpolation is superior. For small values of T/τ, both parabolic interpolation and Lorentzian interpolation of the absorption line shape give greater errors than no interpolation. For interpolation of the magnitude lineshape, interpolation with the “magnitude-Lorentzian” function gives the exact frequency of the continuous spectrum. This interpolation procedure permits exact determination of the true frequency and true intensity for both absorption mode and magnitude mode FT spectra.

The Research of NURBS Curve Interpolation Algorithm Based on Parabolic and the First-Order Taylor Expansion Interpolation Algorithm

2014 ◽  
Vol 1003 ◽  
pp. 260-263
Author(s):  
Zhi Qiang Zhang ◽  
Wen Jin Wang ◽  
Jing Zhang ◽  
Jian Zhao ◽  
Li Ying Sun ◽  
...  
Keyword(s):  
Surface Quality ◽  
Taylor Expansion ◽  
Interpolation Error ◽  
Interpolation Algorithm ◽  
Nurbs Curve ◽  
First Order ◽  
Parabolic Interpolation ◽  
Curve Interpolation ◽  
Part Surface ◽  
Current Point

The NURBS curve interpolation algorithm based on parabolic interpolation error and the first-order Taylor expansion interpolation algorithm is proposed to improve part surface quality and chord error of NURBS curve interpolation algorithm. The part surface quality is improved effectively by the parabolic interpolation algorithm in the conduction that the previous point, the current point and the next point which was computed by the first order Taylor expansion interpolation algorithm were known. The effectiveness of this algorithm is proved by the NURBS curve interpolation simulation.

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