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pyshsjkpg.html
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<title>SHTOOLS - Localized spectral analysis</title>
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<h1 id="shsjkpg">SHSjkPG</h1>
<p>Calculate the expectation of the product of two functions, each multiplied by a different data taper, for a given spherical harmonic degree and two different angular orders.</p>
<h1 id="usage">Usage</h1>
<p><code>value</code> = pyshtools.SHSjkPG (<code>incspectra</code>, <code>l</code>, <code>m</code>, <code>mprime</code>, <code>hj_real</code>, <code>hk_real</code>, <code>mj</code>, <code>mk</code>, <code>lwin</code>, <code>hkcc</code>)</p>
<h1 id="returns">Returns</h1>
<dl>
<dt><code>value</code> : complex</dt>
<dd>The expectation of the product of two functions, each multiplied by a different data taper, for a given spherical harmonic degree and two different angular orders.
</dd>
</dl>
<h1 id="parameters">Parameters</h1>
<dl>
<dt><code>incspectra</code> : float, dimension (<code>l</code>+<code>lwin</code>+1)</dt>
<dd>The global cross-power spectrum of <code>f</code> and <code>g</code>.
</dd>
<dt><code>l</code> : integer</dt>
<dd>The spherical harmonic degree for which to calculate the expectation.
</dd>
<dt><code>m</code> : integer</dt>
<dd>The angular order of the first localized function, <code>Phi</code>.
</dd>
<dt><code>mprime</code> : integer</dt>
<dd>The angular order of the second localized function, <code>Gamma</code>.
</dd>
<dt><code>hj_real</code> : float, dimension (<code>lwin</code>+1)</dt>
<dd>The real spherical harmonic coefficients of angular order <code>mj</code> used to localize the first function <code>f</code>. These are obtained by a call to <code>SHReturnTapers</code>.
</dd>
<dt><code>hk_real</code> : float, dimension (<code>lwin</code>+1)</dt>
<dd>The real spherical harmonic coefficients of angular order <code>mk</code> used to localize the second function <code>g</code>. These are obtained by a call to <code>SHReturnTapers</code>.
</dd>
<dt><code>mj</code> : integer</dt>
<dd>The angular order of the window coefficients <code>hj_real</code>.
</dd>
<dt><code>mk</code> : integer</dt>
<dd>The angular order of the window coefficients <code>hk_real</code>.
</dd>
<dt><code>lwin</code> : integer</dt>
<dd>the spherical harmonic bandwidth of the localizing windows <code>hj_real</code> and <code>hk_real</code>.
</dd>
<dt><code>hkcc</code> : integer</dt>
<dd>If 1, the function described in the <code>description</code> will be calculated as is. If 2, the second localized function <code>Gamma</code> will not have its complex conjugate taken.
</dd>
</dl>
<h1 id="description">Description</h1>
<p><code>SHSjkPG</code> will calculate the expectation of two functions (<code>f</code> and <code>g</code>), each localized by a different data taper that is a solution of the spherical cap concentration problem, for a given spherical harmonic degree and two different angular orders. As described in Wieczorek and Simons (2007), this is the function</p>
<pre><code> / m(j) mprime(k)* \
| Phi Gamma |
\ l l /</code></pre>
<p>The global cross-power spectrum of <code>f</code> and <code>g</code> is input as <code>incspectra</code>, and the real coefficients of the two data tapers of angular order <code>mj</code> and <code>mk</code> (obtained by a call to <code>SHReturnTapers</code>) are specified by <code>hj_real</code> and <code>hk_real</code>. If <code>hkcc</code> is set to 1, then the above function is calculated as is. However, if this is set to 2, then the complex conjugate of the second localized function is not taken.</p>
<h1 id="references">References</h1>
<p>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.</p>
<h1 id="see-also">See also</h1>
<p><a href="pyshreturntapers.html">shreturntapers</a>, <a href="pyshmtvaropt.html">shmtvaropt</a></p>
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<td class="c1"><a href="http://www.ipgp.fr/">Institut de Physique du Globe de Paris</a></td>
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