Direct power spectral density estimation from structure functions without Fourier transforms

Fuente: arXiv
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Autores principales: Bishop, Mark A., Oughton, Sean, Parashar, Tulasi N., Perrott, Yvette C.
Formato: Preprint
Publicado: 2026
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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