Fast spherical harmonic transforms
WebJul 31, 2024 · 4 fast vector spherical harmonic transforms In Subsections 4.1 and 4.2 below, we prov e two theorems to represent the vector spherical harmonic transforms by scalar spherical harmonics and Clebsch ... WebThe SSHT code provides functionality to perform fast and exact spin spherical harmonic transforms based on the sampling theorem on the sphere derived in McEwen & …
Fast spherical harmonic transforms
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WebJan 21, 2013 · The fast Fourier transform (FFT) should be used for this part, as it improves accuracy and speed. SHTns uses the FFTW library [ Frigo & Johnson, 2005 ], a portable, … WebWe develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at using only samples. We obtain the optimal number of samples…
WebM.P. Mohlenkamp, A fast transform for spherical harmonics, J. Fourier Anal. Appl. 5 (2/3) (1999) 159–184. Google Scholar S. Moore, Efficient stabilization methods for fast polynomial transforms, Ph.D. thesis, Department of Mathematics and Computer Science, Dartmouth College (1994). WebJan 17, 2024 · It implements the novel spherical harmonic transform (NSHT) of a band-limited signal using the optimal number of samples. ... Z. Khalid, R. A. Kennedy and J. D. McEwen, “An Optimal-Dimensionality Sampling Scheme on the Sphere for Fast Spherical Harmonic Transforms,” IEEE Trans. Signal Process., vol. 62, no. 17, pp. 4597-4610, …
WebThe spherical harmonic transform (SHT) is the spher-ical analog of the Fourier transform, and is an essential tool for data analysis and simulation on the sphere. A scalar field f(θ,φ) on the unit sphere can be expressed as a weighted sum of the spherical harmonic basis functions Yℓm(θ,φ), f(θ,φ) = X∞ ℓ=0 Xℓ m=−ℓ aℓmYℓm ... WebIn physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency.The term Fourier transform refers to both this complex-valued function and the mathematical …
WebThe spectral synthesis and analysis algorithms using fast Fourier transforms and Legendre transforms with the associated Legendre functions are presented in detail. A set of methods associated with a spectral_field class provides spectral approximation to the differential operators ∇ ⋯, ∇ ×, ∇, and ∇ 2 in spherical geometry.
http://sun.stanford.edu/~tplarson/NoiseModel.pdf metabase or supersetWebMar 1, 2005 · The fast spherical harmonic transform algorithm proposed by Suda and Takami is evaluated in the solutions of the shallow water equation test set defined by … metabase machine learningWebApr 24, 2024 · Mathematica's implementation of the Fast Fourier Transform is, naturally, much faster than computing the discrete transform yourself using Sum. The analog of the Fourier transform of a function f … how tall is willie nelson and weightWebJun 3, 2016 · SHTns is a high performance library for Spherical Harmonic Transform written in C, aimed at numerical simulation (fluid flows, mhd, ...) in spherical geometries. … metabase pricingWebFeb 15, 2012 · The spherical harmonic transform (SHT) is the spherical analog of the Fourier transform and is an essential tool for data analysis and simulation on the … how tall is william wallaceWebSpherical harmonic expansions are a well-understood and widely used tool of applied math- ematics; they are encountered, inter alia, in weather and climate modeling, in … how tall is william mapotherWebOct 1, 2013 · This article describes the implementation of a practical fast spherical harmonics transform into the Integrated Forecast System (IFS) at ECMWF. Details of … metabase optional variable