The impact of Fourier series: the discussion over Riemann integrable functions, Dirichlet kernel, and good kernel

Yuheng Yue

doi:10.1117/12.2672722

28 March 2023 The impact of Fourier series: the discussion over Riemann integrable functions, Dirichlet kernel, and good kernel

Yuheng Yue

Author Affiliations +

Proceedings Volume 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022); 125970L (2023) https://doi.org/10.1117/12.2672722
Event: Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 2022, Nanjing, China

Abstract

In this article, the properties of Fourier Series by discussing around the basic properties of integrable functions and kernel are discussed. With the discussion over the function f around discontinuities, it is found that f should at least be Reimann integrable functions to make Fourier series imitate the function successfully. More, about the filters, it is clear that the sharp filters will converge to f under a certain condition, with the analyzation over Dirichlet Kernel, and how the convergent becomes successful with the properties over good kernel.

Citation Download Citation

Yuheng Yue "The impact of Fourier series: the discussion over Riemann integrable functions, Dirichlet kernel, and good kernel", Proc. SPIE 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 125970L (28 March 2023); https://doi.org/10.1117/12.2672722

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available