HOME | DOWNLOAD | DOCUMENTATION | FAQ |
> Home > Documentation > Python > Global and Localized Spectral Analysis
SHMTVarOpt
Calculate the minimum variance and corresponding optimal weights of a localized multitaper spectral estimate.
Usage
var_opt
, var_unit
, weight_opt
= SHMTVarOpt (l
, tapers
, taper_order
, sff
, [lwin
, kmax
, nocross
])
Returns
var_opt
: float, dimension (kmax
)- The minimum variance of the multitaper spectral estimate for degree
l
using 1 throughkmax
tapers. var_unit
: float, dimension (kmax
)- The variance of the multitaper spectral estimate using equal weights for degree
l
using 1 throughkmax
tapers. weight_opt
: float, dimension (kmax
,kmax
)- The optimal weights (in columns) that minimize the multitaper spectral estimate's variance using 1 through
kmax
tapers.
Parameters
l
: integer- The angular degree to determine the minimum variance and optimal weights.
tapers
: float, dimension (lwinin
+1,kmaxin
)- A matrix of localization functions obtained from
SHReturnTapers
orSHReturnTapersM
. taper_order
: integer, dimension (kmaxin
)- The angular order of the windowing coefficients in TAPERS. If this matrix was created using
SHReturnTapersM
, then this array must be composed of zeros. sff
: float, dimension (l
+lwinin
+1)- The global unwindowed power spectrum of the function to be localized.
lwin
: optional, integer, default =lwinin
- The spherical harmonic bandwidth of the localizing windows.
kmax
: optional, integer, default =kmaxin
- The maximum number of tapers to be used when calculating the minimum variance and optimal weights.
nocross
: optional, integer, default = 0- If 1, only the diagonal terms of the covariance matrix Fij will be computed. If 0, all terms will be computed.
Description
SHMTVarOpt
will determine the minimum variance that can be achieved by a weighted multitaper spectral analysis, as is described by Wieczorek and Simons (2007). The minimum variance is output as a function of the number of tapers utilized, from 1 to a maximum of kmax
, and the corresponding variance using equal weights is output for comparison. The windowing functions are assumed to be solutions to the spherical-cap concentration problem, as determined by a call to SHReturnTapers
or SHReturnTapersM
. The minimum variance and weights are dependent upon the form of the global unwindowed power spectrum, Sff
.
If the optional argument nocross
is set to 1, then only the diagnonal terms of Fij
will be computed.
References
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.
See also
shreturntapers, shreturntapersm, shmultitaperse, shmultitapercse; shlocalizedadmitcorr, shbiasadmitcorr, shbiask, shmtdebias
> Home > Documentation > Python > Global and Localized Spectral Analysis
Laboratoire Lagrange | Observatoire de la Côte d'Azur | © 2016 SHTOOLS |