<html><head><style type='text/css'>p { margin: 0; }</style></head><body><div style='font-family: times new roman,new york,times,serif; font-size: 12pt; color: #000000'><p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;">Thanks Rafael (and Antoine as well)<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;"> </span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;">Now I think I understand what went wrong <o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;"> </span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;">Paul<o:p></o:p></span></font></p><br><hr id="zwchr"><div style="color:#000;font-weight:normal;font-style:normal;text-decoration:none;font-family:Helvetica,Arial,sans-serif;font-size:12pt;"><b>De: </b>"Rafael Guerra" <jrafaelbguerra@hotmail.com><br><b>À: </b>"Users mailing list for Scilab" <users@lists.scilab.org><br><b>Envoyé: </b>Jeudi 29 Septembre 2016 13:38:09<br><b>Objet: </b>Re: [Scilab-users] shift phase in fft<br><br>
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<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">Hi Paul,</span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black"> </span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">Your phase rotation seems to be working fine but the
<span class="SpellE">fft</span> output is complex and only the real part is plotted by Scilab and that is why the resulting amplitude seems to be smaller.</span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black"> </span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">If you want to have your output real, one way is may be to handle separately the positive and negative frequencies as
follows:</span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black"> </span></font></p>
<pre><span class="SpellE"><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#AE5CB0">clf</span></font></u></span><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">()</span></font><font color="black" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">;</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"></span></font></pre>
<pre><font size="2" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> </span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">f</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="rosybrown"><span style="color:rosybrown">10</span></font><font color="black"><span style="color:black">;</span></font> <i><font color="#64ae64"><span style="color:#64AE64;font-style:italic">// frequency</span></font></i></span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">omega</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="rosybrown"><span style="color:rosybrown">2</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">*</span></font><font color="orchid"><span style="color:orchid">%pi</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">*</span></font><font color="black"><span style="color:black">f;</span></font> <i><font color="#64ae64"><span style="color:#64AE64;font-style:italic">// circular frequency</span></font></i></span></font></pre>
<pre><span class="SpellE"><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">nb_T</span></font></span><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="rosybrown"><span style="color:rosybrown">5</span></font><font color="black"><span style="color:black">;</span></font> <i><font color="#64ae64"><span style="color:#64AE64;font-style:italic">// number of periods</span></font></i></span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">t1</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="rosybrown"><span style="color:rosybrown">0</span></font><font color="black"><span style="color:black">;</span></font></span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">t2</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="#4a55db"><span style="color:#4A55DB">(</span></font><span class="SpellE"><font color="black"><span style="color:black">nb_T</span></font></span> <font color="#5c5c5c"><span style="color:#5C5C5C">/</span></font> <font color="black"><span style="color:black">f</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font><font color="black"><span style="color:black">;</span></font></span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">n</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="rosybrown"><span style="color:rosybrown">10</span></font><font color="black"><span style="color:black">;</span></font></span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">t</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <span class="SpellE"><u><font color="#ae5cb0"><span style="color:#AE5CB0">linspace</span></font></u></span><font color="#4a55db"><span style="color:#4A55DB">(</span></font><font color="black"><span style="color:black">t1,t2,</span></font><font color="rosybrown"><span style="color:rosybrown">2</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">^</span></font><font color="black"><span style="color:black">n</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">'</span></font><font color="black"><span style="color:black">;</span></font> <i><font color="#64ae64"><span style="color:#64AE64;font-style:italic">// must be a power of 2</span></font></i></span></font></pre>
<pre><span class="SpellE"><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">nl</span></font></span><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="#32b9b9"><span style="color:#32B9B9">size</span></font><font color="#4a55db"><span style="color:#4A55DB">(</span></font><font color="black"><span style="color:black">t,</span></font><font color="rosybrown"><span style="color:rosybrown">"*"</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font><font color="black"><span style="color:black">;</span></font></span></font></pre>
<pre><font size="2" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> </span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">s1</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="rosybrown"><span style="color:rosybrown">2</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">*</span></font><font color="#32b9b9"><span style="color:#32B9B9">sin</span></font><font color="#4a55db"><span style="color:#4A55DB">(</span></font><font color="black"><span style="color:black">omega</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">*</span></font><font color="black"><span style="color:black">t</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font><font color="black"><span style="color:black">;</span></font> <i><font color="#64ae64"><span style="color:#64AE64;font-style:italic">// original signal</span></font></i></span></font></pre>
<pre><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#AE5CB0">plot</span></font></u><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">(</span></font><font color="black" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">t,s1,</span></font><font color="rosybrown" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:rosybrown">"r"</span></font><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">)</span></font><font color="black" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">;</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"></span></font></pre>
<pre><font size="2" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> </span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">phi</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="orchid"><span style="color:orchid">%pi</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">/</span></font><font color="rosybrown"><span style="color:rosybrown">3</span></font><font color="black"><span style="color:black">;</span></font></span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">s2</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="rosybrown"><span style="color:rosybrown">2</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">*</span></font><font color="#32b9b9"><span style="color:#32B9B9">sin</span></font><font color="#4a55db"><span style="color:#4A55DB">(</span></font><font color="black"><span style="color:black">omega</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">*</span></font><font color="black"><span style="color:black">t</span></font> <font color="#5c5c5c"><span style="color:#5C5C5C">+</span></font> <font color="black"><span style="color:black">phi</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font><font color="black"><span style="color:black">;</span></font> <i><font color="#64ae64"><span style="color:#64AE64;font-style:italic">// <span class="SpellE">targetted</span> signal to be rebuilt</span></font></i></span></font></pre>
<pre><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#AE5CB0">plot</span></font></u><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">(</span></font><font color="black" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">t,s2,</span></font><font color="rosybrown" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:rosybrown">"b"</span></font><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">)</span></font><font color="black" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">;</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"></span></font></pre>
<pre><font size="2" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> </span></font></pre>
<pre><i><font size="2" color="#64ae64" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#64AE64;font-style:italic">// shift phase in the <span class="SpellE">fft</span></span></font></i><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"></span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">s1_fft</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <span class="SpellE"><font color="#32b9b9"><span style="color:#32B9B9">fft</span></font></span><font color="#4a55db"><span style="color:#4A55DB">(</span></font><font color="black"><span style="color:black">s1</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font><font color="black"><span style="color:black">;</span></font></span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">s1_fft</span></font><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">(</span></font><font color="rosybrown" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:rosybrown">1</span></font><font color="#ffaa00" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#FFAA00">:</span></font><font color="black" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">nl</span></font><font color="#5c5c5c" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#5C5C5C">/</span></font><font color="rosybrown" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:rosybrown">2</span></font><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">)</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="black"><span style="color:black">s1_fft</span></font><font color="#4a55db"><span style="color:#4A55DB">(</span></font><font color="rosybrown"><span style="color:rosybrown">1</span></font><font color="#ffaa00"><span style="color:#FFAA00">:</span></font><font color="black"><span style="color:black">nl</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">/</span></font><font color="rosybrown"><span style="color:rosybrown">2</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font> <font color="#5c5c5c"><span style="color:#5C5C5C">.*</span></font> <span class="SpellE"><font color="#32b9b9"><span style="color:#32B9B9">exp</span></font></span><font color="#4a55db"><span style="color:#4A55DB">(</span></font><font color="orchid"><span style="color:orchid">%<span class="SpellE">i</span></span></font><font color="#5c5c5c"><span style="color:#5C5C5C">*</span></font><font color="black"><span style="color:black">phi</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font><font color="black"><span style="color:black">;</span></font></span></font></pre>
<pre><font size="2" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> </span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">s1_fft</span></font><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">(</span></font><span class="SpellE"><font color="black" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">nl</span></font></span><font color="#5c5c5c" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#5C5C5C">/</span></font><font color="rosybrown" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:rosybrown">2</span></font><font color="#ffaa00" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#FFAA00">:$</span></font><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">)</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <font color="black"><span style="color:black">s1_fft</span></font><font color="#4a55db"><span style="color:#4A55DB">(</span></font><span class="SpellE"><font color="black"><span style="color:black">nl</span></font></span><font color="#5c5c5c"><span style="color:#5C5C5C">/</span></font><font color="rosybrown"><span style="color:rosybrown">2</span></font><font color="#ffaa00"><span style="color:#FFAA00">:$</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font> <font color="#5c5c5c"><span style="color:#5C5C5C">.*</span></font> <span class="SpellE"><font color="#32b9b9"><span style="color:#32B9B9">exp</span></font></span><font color="#4a55db"><span style="color:#4A55DB">(</span></font><font color="#5c5c5c"><span style="color:#5C5C5C">-</span></font><font color="orchid"><span style="color:orchid">%<span class="SpellE">i</span></span></font><font color="#5c5c5c"><span style="color:#5C5C5C">*</span></font><font color="black"><span style="color:black">phi</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font><font color="black"><span style="color:black">;</span></font></span></font></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">s1_new</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"> <font color="#5c5c5c"><span style="color:#5C5C5C">=</span></font> <span class="SpellE"><u><font color="#ae5cb0"><span style="color:#AE5CB0">ifft</span></font></u></span><font color="#4a55db"><span style="color:#4A55DB">(</span></font><font color="black"><span style="color:black">s1_fft</span></font><font color="#4a55db"><span style="color:#4A55DB">)</span></font><font color="black"><span style="color:black">;</span></font></span></font></pre>
<pre><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:10.0pt;mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#AE5CB0">plot</span></font></u><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">(</span></font><font color="black" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">t,s1_new,</span></font><font color="rosybrown" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:rosybrown">"--g"</span></font><font color="#4a55db" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:#4A55DB">)</span></font><font color="black" face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif;color:black">;</span></font><font face="Monospaced"><span style="mso-bidi-font-size:12.0pt;font-family:"Monospaced",serif"></span></font></pre>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black"> </span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black"> </span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">Regards,</span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">Rafael</span></font></p>
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