Perform a localized multitaper spectral analysis using arbitrary windows derived from a mask.
sd = SHMultiTaperMaskSE (
mtse: float dimension (
- The localized multitaper power spectrum estimate.
sd: float, dimension (
- The standard error of the localized multitaper power spectral estimates.
sh: float, dimension (2,
- The spherical harmonic coefficients of the function to be localized.
tapers: float, dimension ((
- An array of the
kwindowing functions, arranged in columns, obtained from a call to
SHReturnTapersMap. The spherical harmonic coefficients are packed according to the conventions in
lmax: optional, integer, default =
- The spherical harmonic bandwidth of
sh. This must be less than or equal to
lmaxt: optional, integer, default =
- The spherical harmonic bandwidth of the windowing functions in the array
k: optional, integer, default =
- The number of tapers to be utilized in performing the multitaper spectral analysis.
taper_wt: optional, float, dimension (
kin), default = -1
- The weights used in calculating the multitaper spectral estimates and standard error. Optimal values of the weights (for a known global power spectrum) can be obtained from the routine
SHMTVarOpt. The default value specifies not to use
norm: optional, integer, default = 1
- 1 (default) = 4-pi (geodesy) normalized harmonics; 2 = Schmidt semi-normalized harmonics; 3 = unnormalized harmonics; 4 = orthonormal harmonics.
csphase: optional, integer, default = 1
- 1 (default) = do not apply the Condon-Shortley phase factor to the associated Legendre functions; -1 = append the Condon-Shortley phase factor of (-1)^m to the associated Legendre functions.
SHMultiTaperMaskSE will perform a localized multitaper spectral analysis of an input function expressed in spherical harmonics using an arbitrary set of windows derived from a mask. The maximum degree of the localized multitaper cross-power spectrum estimate is
lmax-lmaxt. The matrix
tapers contains the spherical harmonic coefficients of the windows and can be obtained by a call to
SHReturnTapersMap. The coefficients of each window are stored in a single column, ordered according to the conventions used in
If the optional array
taper_wt is specified, these weights will be used in calculating a weighted average of the individual
k tapered estimates
mtse and the corresponding standard error of the estimates
sd. If not present, the weights will all be assumed to be equal. When
taper_wt is not specified, the mutltitaper spectral estimate for a given degree is calculated as the average obtained from the
k individual tapered estimates. The standard error of the multitaper estimate at degree
l is simply the population standard deviation,
S = sqrt(sum (Si - mtse)^2 / (k-1)), divided by
sqrt(k). See Wieczorek and Simons (2007) for the relevant expressions when weighted estimates are used.
The employed spherical harmonic normalization and Condon-Shortley phase convention can be set by the optional arguments
csphase; if not set, the default is to use geodesy 4-pi normalized harmonics that exclude the Condon-Shortley phase of (-1)^m.
Wieczorek, M. A. and F. J. Simons, Minimum-variance multitaper spectral estimation on the sphere, J. Fourier Anal. Appl., 13, doi:10.1007/s00041-006-6904-1, 665-692, 2007.