Transformation of Water Wave Spectra into Time Series of Surface Elevation
Abstract
:1. Introduction
2. Fourier Analysis Background
- Axiom 1:
- x is a real-valued function if and only if the Fourier transform of x is Hermitian;
- Axiom 2:
- x is a Hermitian function if and only if the Fourier transform of x is real-valued.
3. Transformation of the Spectrum
Oleinik, P.H.; Tavares, G.P.; Machado, B.N.; Isoldi, L.A. Transformation of Water Wave Spectra into Time Series of Surface Elevation: base implementation. Earth 2021, 1, 1–9. Available online: https://gist.github.com/PhelypeOleinik/39803f2385a18d0e86dc3ff8fe02af7b (accessed on 18 September 2021).
4. Verification of the Method
4.1. Verification of Average Values
4.2. Reversing the Process to Obtain the Spectrum from
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Oleinik, P.H.; Tavares, G.P.; Machado, B.N.; Isoldi, L.A. Transformation of Water Wave Spectra into Time Series of Surface Elevation. Earth 2021, 2, 997-1005. https://doi.org/10.3390/earth2040059
Oleinik PH, Tavares GP, Machado BN, Isoldi LA. Transformation of Water Wave Spectra into Time Series of Surface Elevation. Earth. 2021; 2(4):997-1005. https://doi.org/10.3390/earth2040059
Chicago/Turabian StyleOleinik, Phelype Haron, Gabriel Pereira Tavares, Bianca Neves Machado, and Liércio André Isoldi. 2021. "Transformation of Water Wave Spectra into Time Series of Surface Elevation" Earth 2, no. 4: 997-1005. https://doi.org/10.3390/earth2040059