Exploring the Potential of Mixed Fourier Series in Signal Processing Applications Using One-Dimensional Smooth Closed-Form Functions with Compact Support: A Comprehensive Tutorial

This paper studies and analyzes the approximation of one-dimensional smooth closed-form functions with compact support using a mixed Fourier series (i.e., a combination of partial Fourier series and other forms of partial series). To explore the potential of this approach, we discuss and revise its...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical and computational applications 2023-09, Vol.28 (5), p.93
Main Authors: Páez-Rueda, Carlos-Iván, Fajardo, Arturo, Pérez, Manuel, Yamhure, German, Perilla, Gabriel
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Closed form solutions
convergence acceleration
Data compression
Differential equations
Exact solutions
Explicit knowledge
exponential accuracy
Fourier series
Fourier transforms
function reconstruction
Gibbs phenomenon
Harmonic analysis
Harmony (Music)
Interpolation
Inverse problems
Methods
Numerical integration
Polynomials
Signal processing
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper studies and analyzes the approximation of one-dimensional smooth closed-form functions with compact support using a mixed Fourier series (i.e., a combination of partial Fourier series and other forms of partial series). To explore the potential of this approach, we discuss and revise its application in signal processing, especially because it allows us to control the decreasing rate of Fourier coefficients and avoids the Gibbs phenomenon. Therefore, this method improves the signal processing performance in a wide range of scenarios, such as function approximation, interpolation, increased convergence with quasi-spectral accuracy using the time domain or the frequency domain, numerical integration, and solutions of inverse problems such as ordinary differential equations. Moreover, the paper provides comprehensive examples of one-dimensional problems to showcase the advantages of this approach.
ISSN:2297-8747
1300-686X
2297-8747
DOI:10.3390/mca28050093