scholarly journals Rational Approximation on Exponential Meshes

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1999
Author(s):  
Umberto Amato ◽  
Biancamaria Della Vecchia
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Error Estimates ◽  
Rational Approximation ◽  
Exponential Type ◽  
Rational Curves ◽  
Modeling Technique ◽  
Pointwise Approximation ◽  
Type Curves

Error estimates of pointwise approximation, that are not possible by polynomials, are obtained by simple rational operators based on exponential-type meshes, improving previous results. Rational curves deduced from such operators are analyzed by Discrete Fourier Transform and a CAGD modeling technique for Shepard-type curves by truncated DFT and the PIA algorithm is developed.

ERROR ESTIMATES FOR A CLASS OF INTEGRAL AND DISCRETE TRANSFORMS

2000 ◽  
Vol 36 (3-4) ◽  
pp. 291-306
Author(s):  
P.E. Ricci ◽  
G. Mastroianni
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Error Estimates ◽  
Error Bounds ◽  
Integral Transforms ◽  
Theoretical Error ◽  
Fourier Trans ◽  
Discrete Transforms

We consider a class of integral transforms which generalize the classical Fourier Trans- form.We erive some theoretical error bounds for the corresponding approximate iscrete transforms,inclu ing the Discrete Fourier Transform.

APPLICATION OF UNCONVENTIONAL METHODS FOR FREQUENCY ANALYSIS IN ACOUSTICS

Akustika ◽  
2020 ◽  
Vol 36 (36) ◽  
pp. 25-32
Author(s):  
Jaroslav Smutný ◽  
Dušan Janoštík ◽  
Viktor Nohál
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Frequency Analysis ◽  
Mathematical Analysis ◽  
Measured Data ◽  
Application Area ◽  
Acoustic Response ◽  
Recommendations For Practice ◽  
Unconventional Methods ◽  
Frequency Area

The goal of this study is to familiarize a wider professional public with not fully known procedures suitable for processing measured data in the frequency area. Described is the use of the so-called Multi-taper method to analyze the acoustic response. This transformation belongs to a group of nonparametric methods outgoing from discrete Fourier transform, and this study includes its mathematical analysis and description. In addition, the use of respective method in a specific application area and recommendations for practice are described.

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