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<span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
<p class="MsoNormal" style="color: rgb(0, 0, 0); font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%;">
<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none">David-you said:</span></span><span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
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<span style="font-size:10.0pt;font-family:"Courier New";mso-fareast-font-family:"Times New Roman";color:black">“The reason for the steps is that you must transform the k and k' values using a simple formula until you obtain k = 0 and k' = 1."<o:p> </o:p></span></p>
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<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
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<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
<p class="MsoNormal" style="color: rgb(0, 0, 0); font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%;">
<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none">The calculation of elliptic integrals is iterative, recursive if you insist,
(not closed form) - <span style="mso-spacerun:yes"> </span>even in the most professional signal-processing language, Matlab (see ‘tol’ input variable). You have hidden the iterations by automatically running (non-stop) a large enough (just 8 here it seems)
values of j in your for-loop. <span style="mso-spacerun:yes"> </span>It does not matter what you call it.</span></span><span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
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<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
<p class="MsoNormal" style="color: rgb(0, 0, 0); font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%;">
<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none">Your design objective (“output”) should not be the poles, but rather the
plot of phase difference (error), of which you only show one final example (the correct 17 extremal frequencies).<span style="mso-spacerun:yes">
</span>If you plotted the error for the different j’s, I think the progression toward a unique-best solution (alternation theorem) might be evident.</span></span><span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
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<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
<p class="MsoNormal" style="color: rgb(0, 0, 0); font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%;">
<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none">I have already said that, as a practical matter, there was nothing wrong
with what you did.<span style="mso-spacerun:yes"> </span></span></span></p>
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<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><span style="mso-spacerun:yes"></span><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span></span></span><span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
<p class="MsoNormal" style="color: rgb(0, 0, 0); font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%;">
<span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none">-Bernie</span></span><span class="MsoHyperlink" style="color: blue;"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:windowtext;mso-color-alt:windowtext;background:#FAFAFA;text-underline:none"><o:p> </o:p></span></span></p>
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