Direct power spectral density estimation from structure functions without Fourier transforms
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910020838359040 |
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| author | Bishop, Mark A. Oughton, Sean Parashar, Tulasi N. Perrott, Yvette C. |
| author_facet | Bishop, Mark A. Oughton, Sean Parashar, Tulasi N. Perrott, Yvette C. |
| contents | Second-order structure functions and power spectral densities are popular tools in the study of statistical properties across scales, particularly for the analysis of turbulent flows. Although intimately related, analyses primarily use one or the other. We introduce a framework for estimating the power spectrum using the second-order structure function without applying Fourier transforms -- enabling one to take advantage of the real-space structure function calculations. We validate and showcase this method, comparing it to classical Fourier power spectrum estimates determined from analytical calculations, fractional Brownian motion, turbulence simulations, and space-physics and astrophysical observations of turbulence. We show that this method is able to robustly obtain the expected power law behaviour where we use turbulence ranges as test-cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02865 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Direct power spectral density estimation from structure functions without Fourier transforms Bishop, Mark A. Oughton, Sean Parashar, Tulasi N. Perrott, Yvette C. Fluid Dynamics Astrophysics of Galaxies Instrumentation and Methods for Astrophysics Solar and Stellar Astrophysics Second-order structure functions and power spectral densities are popular tools in the study of statistical properties across scales, particularly for the analysis of turbulent flows. Although intimately related, analyses primarily use one or the other. We introduce a framework for estimating the power spectrum using the second-order structure function without applying Fourier transforms -- enabling one to take advantage of the real-space structure function calculations. We validate and showcase this method, comparing it to classical Fourier power spectrum estimates determined from analytical calculations, fractional Brownian motion, turbulence simulations, and space-physics and astrophysical observations of turbulence. We show that this method is able to robustly obtain the expected power law behaviour where we use turbulence ranges as test-cases. |
| title | Direct power spectral density estimation from structure functions without Fourier transforms |
| topic | Fluid Dynamics Astrophysics of Galaxies Instrumentation and Methods for Astrophysics Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2602.02865 |