<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=Windows-1252">
<style type="text/css" style="display:none;"> P {margin-top:0;margin-bottom:0;} </style>
</head>
<body dir="ltr">
<div style="font-family: Arial, Helvetica, sans-serif; color: rgb(0, 0, 0);">
<p class="MsoNormal" style="margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<span style="font-family: Arial, sans-serif; font-size: 12pt;"> </span><br>
</p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<span style="font-size:12.0pt;font-family:"Arial",sans-serif">Thanks David- Outstanding<o:p> </o:p></span></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<span style="font-size:12.0pt;font-family:"Arial",sans-serif">The Orchard curve (yellow) looks nearly “Equiripple” (Chebyshev error) and would be that (by the alternation theorem) if it has the right number of extremal frequencies: one more than the number
of degrees of freedom in the design.<span style="mso-spacerun:yes"> </span>It has 16 pole choices and 17 extremals (both ends count) – so Winner!<span style="mso-spacerun:yes">
</span><span style="mso-spacerun:yes"> </span><o:p> </o:p></span></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<span style="font-size:12.0pt;font-family:"Arial",sans-serif">We likely have a prejudice (looks “intentionally esthetic”) for a pretty-looking equiripple response, so keep in mind that the Orchard (like the Weaver shown) in fact shoots rapidly upward beyond
the band edges.<span style="mso-spacerun:yes"> </span>In addition this min-max-error is achieved at the expense of increased error in other regions.<o:p> </o:p></span></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<span style="font-size:12.0pt;font-family:"Arial",sans-serif">I suspect that with the tiny max error of under 0.2 degrees, this all makes little difference. Readers seeking more info on equiripple procedures for background and as applied to digital filter design
might look at my “A New Simplified Equiripple Design Algorithm for FIR Filters” Electronotes 175 August 1989, pp 3-50.
<o:p> </o:p></span></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<span style="font-size:12.0pt;font-family:"Arial",sans-serif">-<span style="mso-spacerun:yes">
</span>Bernie<o:p> </o:p></span></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<p class="MsoNormal" style="font-size: 11pt; margin: 0in 0in 8pt; line-height: 107%; font-family: Calibri, sans-serif;">
<o:p> </o:p></p>
<br>
</div>
</body>
</html>