EN
Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series
Abstract
For a periodic function in the form of a finite-length exponential Fourier series (i.e., a discrete finite Fourier transform), this work derives an analytical solution to the definite integral of the fourth power of the function across its periodic interval.
Keywords
- Integral of the fourth power of a finite exponential Fourier series
- squared error of energies of discrete Fourier transform of two functions
- $L^4$-norm of finite exponential Fourier series
Supporting Institution
N/A
Project Number
N/A
Thanks
Thanks to the God
References
- Boas, R.P., Entire Functions, Academic Press, New York, 1954.
- Bonami, A., Revesz, S. Gy, Failure of Wiener’s property for positive definite periodic functions, Comptes Rendus Mathematique, 346(1)(2008), 39–44.
- Shapiro, H.S., Majorant problems for Fourier coefficients, The Quarterly Journal of Mathematics, 26(1)(1975), 9–18.
- Sharkas, H., Echigo, H., Beamforming Solutions for Efficient Link Setup and Link Maintenance in mmWave Communication Systems, Master’s Thesis, Lund University, Sweden, 2019.
- Wainger, S., A problem of Wiener and the failure of a principle for Fourier series with positive coefficients, Proceedings of the American Mathematical Society, 20(1)(1969), 16–18.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Publication Date
December 31, 2023
Submission Date
December 11, 2022
Acceptance Date
December 8, 2023
Published in Issue
Year 2023 Volume: 15 Number: 2
APA
Sharkas, H. (2023). Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series. Turkish Journal of Mathematics and Computer Science, 15(2), 403-406. https://doi.org/10.47000/tjmcs.1217379
AMA
1.Sharkas H. Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series. TJMCS. 2023;15(2):403-406. doi:10.47000/tjmcs.1217379
Chicago
Sharkas, Hesham. 2023. “Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series”. Turkish Journal of Mathematics and Computer Science 15 (2): 403-6. https://doi.org/10.47000/tjmcs.1217379.
EndNote
Sharkas H (December 1, 2023) Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series. Turkish Journal of Mathematics and Computer Science 15 2 403–406.
IEEE
[1]H. Sharkas, “Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series”, TJMCS, vol. 15, no. 2, pp. 403–406, Dec. 2023, doi: 10.47000/tjmcs.1217379.
ISNAD
Sharkas, Hesham. “Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series”. Turkish Journal of Mathematics and Computer Science 15/2 (December 1, 2023): 403-406. https://doi.org/10.47000/tjmcs.1217379.
JAMA
1.Sharkas H. Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series. TJMCS. 2023;15:403–406.
MLA
Sharkas, Hesham. “Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series”. Turkish Journal of Mathematics and Computer Science, vol. 15, no. 2, Dec. 2023, pp. 403-6, doi:10.47000/tjmcs.1217379.
Vancouver
1.Hesham Sharkas. Solution of Integral of the Fourth Power of a Finite-Length Exponential Fourier Series. TJMCS. 2023 Dec. 1;15(2):403-6. doi:10.47000/tjmcs.1217379
Cited By
Mapping of $L^2 -$norm of Two Multiplied $2\pi-$Periodic Functions to Their Fourier Coefficients (Part II)
Turkish Journal of Mathematics and Computer Science
https://doi.org/10.47000/tjmcs.1424850