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shbias.html
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shbias.html
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
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<title>SHTOOLS - Localized spectral analysis</title>
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<p class="centeredimage"><img src="../../images/logo.jpg" width=894 height=135 alt="SHTOOLS --- Tools for working with spherical harmonics"></p>
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<PRE>
<!-- Manpage converted by man2html 3.0.1 -->
<B>SHBIAS(1)</B> SHTOOLS 3.0 <B>SHBIAS(1)</B>
</PRE>
<H2 class="man">SHBias</H2 class="man"><PRE>
SHBias - Calculate the (cross-)power spectrum expectation of a windowed
function.
</PRE>
<H2 class="man">SYNOPSIS</H2 class="man"><PRE>
SUBROUTINE SHBias ( SHH, LWIN, INCSPECTRA, LDATA, OUTCSPECTRA, SAVE_CG
)
REAL*8 SHH(LWIN+1), INCSPECTRA(LDATA+1),
OUTCSPECTRA(*)
INTEGER LWIN, LDATA
INTEGER, OPTIONAL SAVE_CG
</PRE>
<H2 class="man">DESCRIPTION</H2 class="man"><PRE>
<B>SHBias</B> will calculate the (cross-)power spectrum expectation of a
function multiplied by a localizing window. This is given by equation
35 of Wieczorek and Simons (2005) and equation 2.11 of Wieczorek and
Simons (2007),
<SFG> = Sum_{j=0}^L Shh Sum_{i=|l-j|}^{|l+j|} Sfg (C_{j0i0}^{l0})^2
where <SFG> is the expectation of the localized (cross-)power spectrum,
Shh is the power spectrum of the window bandlimited to degree L, Sfg is
the global unwindowed (cross-)power spectrum, and C is a Clebsch-Gordan
coefficient. The Clebsch-Gordan coefficients are calculated using a
simple relationship to the Wigner 3-j symbols. The maximum calculated
degree of the windowed power spectrum expectation corresponds to the
smaller of (LDATA+LWIN) and SIZE(OUTCSPECTRA)-1. It is implicitly
assumed that the power spectrum of INSPECTRUM is zero beyond degree
LDATA.
If this routine is to be called several times using the same values of
LWIN and LDATA, then the Clebsch-Gordon coefficients can be precomputed
and saved by setting the optional parameter SAVE_CG equal to 1. To
deallocate the saved memory, which is a matrix of size
(LWIN+LDATA,LWIN,2*LWIN+LDATA+1), set SAVE_CG equal to -1.
</PRE>
<H2 class="man">ARGUMENTS</H2 class="man"><PRE>
SHH (input) REAL*8, DIMENSION (LWIN+1)
The power spectrum of the localizing window.
LWIN (input) INTEGER
The spherical harmonic bandwidth of the localizing
window.
INCSPECTRA (input) REAL*8, DIMENSION (LDATA+1)
The global unwindowed (cross-)power spectrum.
LDATA (input) INTEGER
The maximum degree of the global unwindowed power
spectrum.
OUTCSPECTRA (output) REAL*8, DIMENSION (*)
The expectation of the localized (cross-)power spectrum.
The maximum spherical harmonic degree of the output is
min(LDATA+LWIN, SIZE(OUTSCSPECTRA)-1).
SAVE_CG (input) INTEGER, OPTIONAL
If set equal to 1, the Clebsch-Gordon coefficients will
be precomputed and saved for future use (if LWIN or LDATA
change, this will be recomputed). To deallocate the saved
memory, set this parameter equal to 1. If set equal to 0
(default), the Clebsch-Gordon coefficients will be
recomputed for each call.
</PRE>
<H2 class="man">SEE ALSO</H2 class="man"><PRE>
<B>shpowerspectra(1)</B>, <B>shcrosspowerspectra(1)</B>, <B>wigner3j(1)</B>,
<B>shreturntapers(1)</B>, <B>shreturntapersm(1)</B>, <B>shbiasadmitcorr(1)</B>
<http://shtools.ipgp.fr/>
</PRE>
<H2 class="man">REFERENCES</H2 class="man"><PRE>
Wieczorek, M. A. and F. J. Simons, Localized spectral analysis on the
sphere, <B>Geophys.</B> <B>J.</B> <B>Int.</B>, 162, 655-675,
doi:10.1111/j.1365-246X.2005.02687.x, 2005.
Wieczorek, M. A. and F. J. Minimum-variance multitaper spectral
estimation on a sphere, <B>J.</B> <B>Fourier</B> <B>Anal.</B> <B>Appl.</B>, 13, 665-692,
doi:10.1007/s00041-006-6904-1, 2007.
</PRE>
<H2 class="man">COPYRIGHT AND LICENSE</H2 class="man"><PRE>
Copyright 2012 by Mark Wieczorek <wieczor@ipgp.fr>.
This is free software; you can distribute and modify it under the terms
of the revised BSD license.
SHTOOLS 3.0 2014-09-12 <B>SHBIAS(1)</B>
</PRE>
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<table class="footer2" summary = "SHTOOLS; Fortran and Python spherical harmonic transform software package">
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<td class="c1"><a href="http://www.ipgp.fr/">Institut de Physique du Globe de Paris</a></td>
<td class="c2"><a href="http://www.sorbonne-paris-cite.fr/index.php/en">University of Sorbonne Paris Cité</a></td>
<td class="c3">© 2015 <a href="http://www.ipgp.fr/~wieczor">Mark Wieczorek</a></td>
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