<div dir="ltr"><div class="gmail_extra">Hi Jonathan,<br><br><div class="gmail_quote">On Sat, Jun 28, 2014 at 9:40 PM, Jonathan Wilkes via Pd-list <span dir="ltr"><<a href="mailto:pd-list@lists.iem.at" target="_blank">pd-list@lists.iem.at</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div><div style="color:rgb(0,0,0);background-color:rgb(255,255,255);font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:12pt">
<div><div><br><div style="color:rgb(0,0,0);font-family:HelveticaNeue,'Helvetica Neue',Helvetica,Arial,'Lucida Grande',sans-serif;font-size:12pt;background-color:rgb(255,255,255)"><div>Hi list,</div><div>     If I take a circle, cut it in half horizontally, then move the bottom half r*2 units to the right, what is the waveform that results?</div>
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</blockquote></div><br><br><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">A phase corrected triangle wave at least looks like half a circle (the green wave: <a href="http://funsseelen.eu/images/gnuplot_100_1024.png">http://funsseelen.eu/images/gnuplot_100_1024.png</a>).<br>
<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">Partials for a normal triangle wave:<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">1/(1^2) * sin(x) +<br>
</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">0 +<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">-1/(3^2) * sin(3x) +<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">
0 +<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">1/(5^2) * sin(5x) +<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">0 +<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">
-1/(7^2) * sin(7x)<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">et cetera.. --> infinity<br><br><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">Partials for a phase corrected triangle wave:<br>
</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">1/(1^2) * sin(x) +<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">0 +<br>1/(3^2) * sin(3x) +<br>0 +<br>1/(5^2) * sin(5x) +<br>
0 +<br>1/(7^2) * sin(7x) +<br></div>et cetera.. --> infinity<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">
(<a href="http://funsseelen.eu/C/fourier_series/triangle.c">http://funsseelen.eu/C/fourier_series/triangle.c</a> / <a href="http://funsseelen.eu/C/fourier_series/triangle2.c">http://funsseelen.eu/C/fourier_series/triangle2.c</a> C code to calculate samples that create both wave forms)<br>
<br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">Regards,<br><br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">Funs<br></div><br></div></div>