-
Notifications
You must be signed in to change notification settings - Fork 103
/
shmtvar.doc
50 lines (45 loc) · 2.02 KB
/
shmtvar.doc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Calculate the theoretical variance of a multitaper spectral estimate for a given
input power spectrum.
Usage
-----
variance = SHMTVar (l, tapers, taper_order, sff, [kmax, lwin, taper_wt,
nocross])
Returns
-------
variance : float
The variance of the multitaper spectral estimate for degree l.
Parameters
----------
l : integer
The spherical harmonic degree used to calculate the theoretical variance.
tapers : float, dimension (lwinin+1, kmaxin)
A matrix of localization functions obtained from SHReturnTapers or
SHReturnTapersM.
taper_order : integer, dimension (kmaxin)
The angular order of the windowing coefficients in tapers.
sff : float, dimension (l+lwinin+1)
The global unwindowed power spectrum of the function to be localized.
kmax : optional, integer, default = kmaxin
The maximum number of tapers to be used when calculating the variance.
lwin : optional, integer, default = lwinin
The spherical harmonic bandwidth of the localizing windows.
taper_wt : optional, float, dimension (kmaxin)
The weights to be applied to the multitaper spectral estimates.
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
-----------
SHMTVar will determine the theoretical variance of a multitaper spectral
estimate for a given input power spectrum, degree l, and optionally, a set of
taper weights (see eq. C21 of Wieczorek and Simons 2007). The windowing
functions are assumed to be solutions to the spherical-cap concentration
problem, as determined by a call to SHReturnTapers or SHReturnTapersM. If
unweighted_covar is specified, then the unweighted covariance matrix of the kmax
tapers (i.e., Fij) will be output. 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.