Multitaper spectral estimation (spherical cap domain)
| Routine 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)
| Routine name | Description |
|---|---|
| SHReturnTapersMap | Calculate the eigenfunctions of the concentration problem for an arbitrary concentration region. |
| SHMultiTaperMaskSE | Perform a localized multitaper spectral analysis using arbitrary windows. |
| SHMultiTaperMaskCSE | Perform a localized multitaper cross-spectral analysis using arbitrary windows. |
| SHBiasKMask | Calculate the multitaper (cross-)power spectrum expectation of a function localized by arbitrary windows derived from a mask. |
| 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)
| Routine 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 for a given spherical harmonic degree. |
Other routines
| Routine 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.