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      <title>TABRND1</title>
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      <div class="title_refTopic" id="xps10_pagetitle">TABRND1 </div>
      <hr noshade="true">
      <h4 class="refClassification">Power Spectral Density Table </h4>
      <p class="para_refTopic">Defines power spectral density as a tabular function of frequency for use in random analysis.  Referenced by the RANDPS entry. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="11.79*">
               <col span="1" width="10.08*">
               <col span="1" width="10.08*">
               <col span="1" width="10.08*">
               <col span="1" width="10.08*">
               <col span="1" width="10.08*">
               <col span="1" width="10.08*">
               <col span="1" width="10.08*">
               <col span="1" width="8.55*">
               <col span="1" width="9.12*">
            </colgroup>
            <thead>
               <tr>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">1 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">2 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">3 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">4 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">5 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">6 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">7 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">8 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">9 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">10 </p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">TABRND1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">TID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">XAXIS </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">YAXIS </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">f1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">g1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">f2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">g2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">f3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">g3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">-etc.- </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Example: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="11.42*">
               <col span="1" width="10.09*">
               <col span="1" width="10.09*">
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               <col span="1" width="10.09*">
               <col span="1" width="10.09*">
               <col span="1" width="10.09*">
               <col span="1" width="10.09*">
               <col span="1" width="10.09*">
               <col span="1" width="7.82*">
            </colgroup>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">TABRND1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">2.5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">.01057 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">2.6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">.01362 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ENDT </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Fields:</div>
      <div class="refCategoryContent">
         <table cellpadding="9" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="18.46*">
               <col span="1" width="81.54*">
            </colgroup>
            <thead>
               <tr>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Field </b></p>
                  </th>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Contents </b></p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">TID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Table identification number.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">XAXIS </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Specifies a linear or logarithmic interpolation for the x-axis.  (Character:  &ldquo;LINEAR&rdquo; or &ldquo;LOG&rdquo;; Default=&ldquo;LINEAR&rdquo;) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">YAXIS </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Specifies a linear or logarithmic interpolation for the y-axis.  (Character:  &ldquo;LINEAR&rdquo; or &ldquo;LOG&rdquo;; Default=&ldquo;LINEAR&rdquo;) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">fi </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Frequency value in cycles per unit time.  (Real &ge; 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">gi </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Power spectral density.  (Real) </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Remarks: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">The fi must be in either ascending or descending order, but not both. </p>
            </li>
            <li>
               <p class="para_item">Discontinuities may be specified between any two points except the two starting points or two end points.  For example, in <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_14.html#ref61351');return(false);">Figure 19-</a> discontinuities are allowed only between points f2 through f7.  Also, if g is evaluated at a discontinuity, then the average value of g is used.  In <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_14.html#ref61351');return(false);">Figure 19-</a>, the value of g at f=f3 is <em>g</em>=(<em>g</em>3+<em>g</em>4) / 2. If the y-axis is a LOG axis then the jump at the discontinuity is evaluated as <img align="bottom" src="graphics/bulktuv-equ25.gif" border="0">. 
               </p>
            </li>
            <li>
               <p class="para_item">At least two entries must be present. </p>
            </li>
            <li>
               <p class="para_item">Any fi-gi pair may be ignored by placing &ldquo;SKIP&rdquo; in either of the two fields used for that entry. </p>
            </li>
            <li>
               <p class="para_item">The end of the table is indicated by the existence of &ldquo;ENDT&rdquo; in either of the two fields following the last entry.  An error is detected if any continuations follow the entry containing the end-of-table flag &ldquo;ENDT&rdquo;. </p>
            </li>
            <li><a name="ref94342"></a><p class="para_item">TABRND1 uses the algorithm </p>
               <p align="center"><img align="bottom" src="graphics/bulktuv-equ26.gif"></p>
               <p class="para_item">where <em>f</em> is input to the table and <em>g</em> is returned.  The table look-up is performed using linear interpolation within the table and linear extrapolation outside the table using the two starting or end points.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_14.html#ref61351');return(false);">Figure 19-</a>.  No warning messages are issued if table data is input incorrectly. 
               </p><a name="ref61351"></a><div class="figure">
                  <p align="center"><img align="bottom" src="graphics/bulktuv-fig09.gif"></p>
               </div>
               <div class="title_figure">Figure. Example of Table Extrapolation and Discontinuity </div>
            </li>
            <li>
               <p class="para_item">For auto spectral density, the value of <em>g</em> returned must be greater than or equal to zero, as shown in Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_14.html#ref94342');return(false);">18-6. </a></p>
            </li>
            <li>
               <p class="para_item">Tabular values on an axis if XAXIS or YAXIS=LOG must be positive.  A fatal message will be issued if an axis has a tabular value &le; 0. </p>
            </li>
            <li>
               <p class="para_item">The algorithms used are: </p>
               <table border="1" cellpadding="9" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="16.38*">
                     <col span="1" width="16.38*">
                     <col span="1" width="67.24*">
                  </colgroup>
                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">XAXIS </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">YAXIS </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">f(x) </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LINEAR </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LINEAR </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulktuv-equ27.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LOG </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LINEAR </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulktuv-equ28.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LINEAR </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LOG </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulktuv-equ29.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LOG </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LOG </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulktuv-equ30.gif"></p>
                        </td>
                     </tr>
                  </tbody>
               </table><br><p class="para_item">where <em>f<sub class="subscript">i</sub> &lt; f &lt; f<sub class="subscript">i+1</sub></em></p>
            </li>
         </ol>
      </div>
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