This module provides routines for performing global spectral analyses, the construction of spatiospectral localization windows, and localized multitaper spectral analyses.
Global spectral analysis
| Function name |
Description |
| 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. |
Multitaper spectral estimation (spherical cap domain)
| Function name |
Description |
| 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. |
Localization windows (arbitrary domain)
| Function name |
Description |
| 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. |
Localization bias (general)
| Function name |
Description |
| SHBias |
Calculate the (cross-)power spectrum expectation of a windowed function. |
Slepian function expansions
| Routine name |
Description |
| 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. |
Other routines
| Function name |
Description |
| SphericalCapCoef |
Calculate the spherical harmonic coefficients of a spherical cap. |
References
- 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.
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