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pysh.spectralanalysis |
spherical harmonics, global spectral analysis, slepian functions, spatiospectral localization windows, localized multitaper spectral analysis, python, pyshtools |
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python-spectral-analysis.html |
This module provides routines for performing global spectral analyses, the construction of spatiospectral localization windows, and localized multitaper spectral analyses. |
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Function name | Description |
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spectrum | Calculate the spectrum of a real or complex function. |
cross_spectrum | Calculate the cross-spectrum of a real or complex function. |
SHAdmitCorr | Calculate the admittance and correlation spectra of two functions. |
SHConfidence | Compute the probability that two sets of spherical harmonic coefficients are correlated at a given degree and for a given correlation coefficient. |
Function name | Description |
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SHMultiTaperSE | Perform a localized multitaper spectral analysis. |
SHMultiTaperCSE | Perform a localized multitaper cross-spectral analysis. |
SHLocalizedAdmitCorr | Calculate the localized admittance and correlation spectra of two functions at a given location. |
SHReturnTapers | Calculate the eigenfunctions of the spherical-cap concentration problem. |
SHReturnTapersM | Calculate the eigenfunctions of the spherical-cap concentration problem for a single angular order. |
ComputeDm | Compute the space-concentration kernel of a spherical cap. |
ComputeDG82 | Compute the tridiagonal matrix of Grünbaum et al. (1982) that commutes with the space-concentration kernel of a spherical cap. |
SHFindLWin | Determine the spherical-harmonic bandwidth that is necessary to achieve a certain concentration factor. |
SHBiasK | Calculate the multitaper (cross-)power spectrum expectation of a windowed function. |
SHMTCouplingMatrix | Calculate the multitaper coupling matrix for a given set of localization windows. |
SHBiasAdmitCorr | Calculate the expected multitaper admittance and correlation spectra associated with the input global cross-power spectra of two functions. |
SHMTDebias | Invert for the global power spectrum given a localized multitaper spectrum estimate. |
SHMTVarOpt | Calculate the theoretical minimum variance of a localized multitaper spectral estimate and the corresponding optimal weights to apply to each localized spectrum. |
SHMTVar | Calculate the theoretical variance of a multitaper spectral estimate for a given input power spectrum. |
SHSjkPG | Calculate the expectation of the product of two functions, each multiplied by a different data taper, for a given spherical harmonic degree and two different angular orders. |
SHRotateTapers | Rotate orthogonal spherical-cap Slepian functions centered at the North pole to a different location. |
Function name | Description |
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SHReturnTapersMap | Calculate the eigenfunctions of the concentration problem for an arbitrary concentration region. |
SHBiasKMask | Calculate the multitaper (cross-)power spectrum expectation of a function localized by arbitrary windows derived from a mask. |
SHMultiTaperMaskSE | Perform a localized multitaper spectral analysis using arbitrary windows. |
SHMultiTaperMaskCSE | Perform a localized multitaper cross-spectral analysis using arbitrary windows. |
ComputeDMap | Compute the space-concentration kernel of a mask defined on the sphere. |
Curve2Mask | Given a set of latitude and longitude coordinates representing a closed curve, output a gridded mask. |
Function name | Description |
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SHBias | Calculate the (cross-)power spectrum expectation of a windowed function. |
Routine name | Description |
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SlepianCoeffs | Determine the expansion coefficients of a function for a given set of input Slepian functions. |
SlepianCoeffsToSH | Convert a function expressed in Slepian coefficients to spherical harmonic coefficients. |
SHSCouplingMatrix | Compute the spherical harmonic coupling matrix for a given set of Slepian functions. |
SHSCouplingMatrixCap | Compute the spherical harmonic coupling matrix for a given set of spherical-cap Slepian functions. |
SHSlepianVar | Calculate the theoretical variance of the power of a function expanded in spherical-cap Slepian functions. |
Function name | Description |
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SphericalCapCoef | Calculate the spherical harmonic coefficients of a spherical cap. |
- Grunbaum, F. A., L. Longhi, and M. Perlstadt, Differential operators commuting with finite convolution integral operators: some non-abelian examples, SIAM J. Appl. Math., 42, 941-955, doi:10.1137/0142067, 1982.