https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Admissible_representation 2026-05-24T05:58:55Z Revision history for this page on the wiki MediaWiki 1.43.0-wmf.28 https://en.formulasearchengine.com/index.php?title=Admissible_representation&diff=17018&oldid=prev 2013-12-09T07:45:25Z

<p>Update deprecated cite parameters using <a href="/index.php?title=Testwiki:AWB&amp;action=edit&amp;redlink=1" class="new" title="Testwiki:AWB (page does not exist)">AWB</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:45, 9 December 2013</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Alyson </del>is the <del style="font-weight: bold; text-decoration: none;">name individuals use to contact me </del>and <del style="font-weight: bold; text-decoration: none;">I believe it sounds fairly great when you say it</del>. <del style="font-weight: bold; text-decoration: none;">For many years he's been residing in Mississippi and he doesn't strategy on changing it</del>. <del style="font-weight: bold; text-decoration: none;">Since he was eighteen he's been operating as an info officer but he ideas on altering it</del>. <del style="font-weight: bold; text-decoration: none;">To perform domino is something I really enjoy performing</del>.&lt;<del style="font-weight: bold; text-decoration: none;">br</del>&gt;&lt;<del style="font-weight: bold; text-decoration: none;">br</del>&gt;<del style="font-weight: bold; text-decoration: none;">Here is my homepage ...  </del>[<del style="font-weight: bold; text-decoration: none;">http</del>://<del style="font-weight: bold; text-decoration: none;">www</del>.<del style="font-weight: bold; text-decoration: none;">january</del>-<del style="font-weight: bold; text-decoration: none;">yjm.com</del>/<del style="font-weight: bold; text-decoration: none;">xe/index</del>.<del style="font-weight: bold; text-decoration: none;">php?mid</del>=<del style="font-weight: bold; text-decoration: none;">video&amp;document_srl</del>=<del style="font-weight: bold; text-decoration: none;">158289 online psychic readings</del>] [<del style="font-weight: bold; text-decoration: none;">http:</del>/<del style="font-weight: bold; text-decoration: none;">/fashionlinked</del>.<del style="font-weight: bold; text-decoration: none;">com/index</del>.<del style="font-weight: bold; text-decoration: none;">php?do</del>=<del style="font-weight: bold; text-decoration: none;">/profile-13453/info/ free psychic] chat online (</del>[http://<del style="font-weight: bold; text-decoration: none;">black7</del>.<del style="font-weight: bold; text-decoration: none;">mireene</del>.com<del style="font-weight: bold; text-decoration: none;">/aqw/5741 Suggested Website</del>]<del style="font-weight: bold; text-decoration: none;">)</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The [[maximum entropy method]] applied to [[spectral density estimation]]. The overall idea </ins>is <ins style="font-weight: bold; text-decoration: none;">that the maximum [[entropy rate]] [[stochastic process]] that satisfies </ins>the <ins style="font-weight: bold; text-decoration: none;">given constant [[autocorrelation]] </ins>and <ins style="font-weight: bold; text-decoration: none;">[[variance]] constraints, is a linear [[Gauss-Markov process]] with [[i</ins>.<ins style="font-weight: bold; text-decoration: none;">i</ins>.<ins style="font-weight: bold; text-decoration: none;">d</ins>.<ins style="font-weight: bold; text-decoration: none;">]] zero-mean, [[Gaussian function|Gaussian]] input</ins>.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Method description==</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The maximum entropy rate, [[strongly stationary]] [[stochastic process]] </ins>&lt;<ins style="font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="font-weight: bold; text-decoration: none;">x_i</ins>&lt;<ins style="font-weight: bold; text-decoration: none;">/math</ins>&gt; <ins style="font-weight: bold; text-decoration: none;">with [</ins>[<ins style="font-weight: bold; text-decoration: none;">autocorrelation]] sequence &lt;math&gt;R_{xx}(k), k = 0,1, \dots P&lt;/math&gt; satisfying the constraints:</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;R_{xx}(k) = \alpha_k&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">for arbitrary constants &lt;math&gt;\alpha_k&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt; is the &lt;math&gt;P&lt;/math&gt;-th order, linear Markov chain of the form:</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:&lt;math&gt;x_i = -\sum_{k=1}^P a_k x_{i-k} + y_i&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">where the &lt;math&gt;y_i&lt;/math&gt; are zero mean, [[i.i.d</ins>.<ins style="font-weight: bold; text-decoration: none;">]] and normally</ins>-<ins style="font-weight: bold; text-decoration: none;">distributed of finite variance &lt;math&gt;\sigma^2&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;</ins>.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Spectral estimation</ins>==</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Given the &lt;math&gt;a_k&lt;/math&gt;, the square of the absolute value of the [[transfer function</ins>]<ins style="font-weight: bold; text-decoration: none;">] of the linear Markov chain model can be evaluated at any required frequency in order to find the [</ins>[<ins style="font-weight: bold; text-decoration: none;">power spectrum]] of &lt;math&gt;x_i&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==References==</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Cover, T. and Thomas, J</ins>. <ins style="font-weight: bold; text-decoration: none;">(1991) Elements of Information Theory, John Wiley and Sons, Inc</ins>.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=<ins style="font-weight: bold; text-decoration: none;">= External links ==</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*kSpectra Toolkit for Mac OS X from </ins>[http://<ins style="font-weight: bold; text-decoration: none;">www</ins>.<ins style="font-weight: bold; text-decoration: none;">spectraworks</ins>.com <ins style="font-weight: bold; text-decoration: none;">SpectraWorks.]  </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Entropy]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Information theory]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Signal processing]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Time series analysis]</ins>]</div></td></tr> </table>

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