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<PRE>
<!-- Manpage converted by man2html 3.0.1 -->
<B>SHBIAS(1)</B>                         SHTOOLS 2.6                        <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),

       &lt;SFG&gt; = Sum_{j=0}^L Shh Sum_{i=|l-j|}^{|l+j|} Sfg (C_{j0i0}^{l0})^2

       where &lt;SFG&gt; 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>

       &lt;http://www.ipgp.jussieu.fr/~wieczor/SHTOOLS/SHTOOLS.html&gt;


</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 2005-2009 by Mark Wieczorek &lt;wieczor@ipgp.fr&gt;.

       This is free software; you can distribute and modify it under the terms
       of the revised BSD license.

SHTOOLS 2.6                       2009-08-18                         <B>SHBIAS(1)</B>
</PRE>

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			<td class="c1"><a href="http://www.cnrs.fr/">Centre National de la Recherche Scientifique</a></td>
			<td class="c2"><a href="http://www.ipgp.jussieu.fr/">Institut de Physique du Globe de Paris</a></td>
			<td class="c3">&copy; 2011 <a href="http://www.ipgp.jussieu.fr/~wieczor">Mark Wieczorek</a></td>
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