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.

DISCRETE TRANSFORM IN BLOCK FORM AND INVARIANCE TO PROCESSING DIRECTION

2021 ◽  
pp. 22-26
Author(s):  
А.Г. Шоберг ◽  
С.В. Сай
Keyword(s):  
Fourier Transform ◽  
Mathematical Models ◽  
Discrete Fourier Transform ◽  
Matrix Representation ◽  
Direction Change ◽  
Block Form ◽  
Discrete Transforms ◽  
Frequency Components ◽  
Block Transforms ◽  
Discrete Transform

Рассмотрен ряд вопросов инвариантности дискретных блочных преобразований. Показано, что смена направления обработки при выполнении обратимых преобразований приводит к изменению, получаемых частотных составляющих. Предложены математические модели блочных дискретных преобразований на основе матричного представления. Предлагается рассматривать дискретные преобразования в зависимости от количества блоков и направления обработки. Приводятся результаты моделирования на основе дискретного преобразования Фурье. Some questions of invariance of a discrete block transforms are considered. It is shown a processing direction change in a reversible transforms performing leads to a frequency components change. Mathematical models are proposed for block discrete transforms based on a matrix representation. The discrete transforms are proposed depending on a blocks number and direction of processing. Modeling results on the discrete Fourier transform are presented.

scholarly journals Exploiting the Symmetry of Integral Transforms for Featuring Anuran Calls

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 405 ◽  
Author(s):  
Amalia Luque ◽  
Jesús Gómez-Bellido ◽  
Alejandro Carrasco ◽  
Julio Barbancho
Keyword(s):  
Machine Learning ◽  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Discrete Cosine Transform ◽  
Integral Transforms ◽  
Machine Learning Techniques ◽  
Classification Algorithms ◽  
Learning Techniques ◽  
Cepstral Coefficients

The application of machine learning techniques to sound signals requires the previous characterization of said signals. In many cases, their description is made using cepstral coefficients that represent the sound spectra. In this paper, the performance in obtaining cepstral coefficients by two integral transforms, Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT), are compared in the context of processing anuran calls. Due to the symmetry of sound spectra, it is shown that DCT clearly outperforms DFT, and decreases the error representing the spectrum by more than 30%. Additionally, it is demonstrated that DCT-based cepstral coefficients are less correlated than their DFT-based counterparts, which leads to a significant advantage for DCT-based cepstral coefficients if these features are later used in classification algorithms. Since the DCT superiority is based on the symmetry of sound spectra and not on any intrinsic advantage of the algorithm, the conclusions of this research can definitely be extrapolated to include any sound signal.

scholarly journals ON THE USE OF DISCRETE FOURIER TRANSFORM FOR SOLVING BIPERIODIC BOUNDARY VALUE PROBLEM OF BIHARMONIC EQUATION IN THE UNIT RECTANGLE

2003 ◽  
Vol 2 (2) ◽  
pp. 37
Author(s):  
A. D. GARNADI
Keyword(s):  
Fourier Transform ◽  
Boundary Value Problem ◽  
Discrete Fourier Transform ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Periodic Sequence ◽  
Trans Form ◽  
One Dimensional ◽  
Fourier Trans

This note is addressed to solving biperiodic boundary value problem of biharmonic equation in the unit rectangle. First, we describe the necessary tools, which is discrete Fourier trans- form for one dimensional periodic sequence, and then extended the results to 2-dimensional biperiodic sequence. Next, we use the discrete Fourier transform 2-dimensional biperiodic sequence to solve discretization of the biperiodic boundary value problem of Biharmonic Equation.

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.

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