<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'>sound interesting ... many thanks for the information<div><br></div><div>Paul<br><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>Vendredi 23 Septembre 2016 13:57:31<br><b>Objet: </b>Re: [Scilab-users] fourier series and fft<br><br>
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<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Hi Paul,</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span lang="PT" style="font-size:11.0pt;mso-ansi-language:PT"><span style="mso-bidi-font-size:10.5pt">Fyi, Tom Co's simple tutorial:
</span></span><a href="http://www.chem.mtu.edu/~tbco/cm416/fft1.pdf" target="_blank"><span lang="PT" style="mso-ansi-language:PT">http://www.chem.mtu.edu/~tbco/cm416/fft1.pdf</span></a></font><span lang="PT" style="mso-ansi-language:PT"></span></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">shows how to obtain the Fourier coefficients via the
<span class="SpellE"><b style="mso-bidi-font-weight:normal"><span style="font-weight:bold;mso-bidi-font-weight:normal">fft</span></b></span></span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Regards,</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Rafael</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">-----Original Message-----<br>
From: users [mailto:users-bounces@lists.scilab.org] On Behalf Of paul.carrico@free.fr<br>
Sent: Friday, September 23, 2016 8:45 AM<br>
To: tim@wescottdesign.com; Users mailing list for Scilab <users@lists.scilab.org><br>
Subject: Re: [Scilab-users] <span class="SpellE">fourier</span> series and <span class="SpellE">
fft</span></span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Thanks Tim for this answer; well I notice I need to "dig" deeper on that topic</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Paul</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt"></span></span></font></p><hr id="zwchr"><p></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">De: "Tim
<span class="SpellE">Wescott</span>" <<a href="mailto:tim@wescottdesign.com" target="_blank"><font color="black"><span style="color:windowtext;text-decoration:none;text-underline:none">tim@wescottdesign.com</span></font></a>></span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">À: "Users mailing list for Scilab" <<a href="mailto:users@lists.scilab.org" target="_blank"><font color="black"><span style="color:windowtext;text-decoration:none;text-underline:none">users@lists.scilab.org</span></font></a>></span></span></font></p>
<p class="MsoPlainText"><span class="SpellE"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Envoyé</span></span></font></span>:
<span class="SpellE">Jeudi</span> 22 <span class="SpellE">Septembre</span> 2016 23:17:27</p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Objet: Re: [Scilab-users]
<span class="SpellE">fourier</span> series and <span class="SpellE">fft</span></span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Hey Paul:</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">If you mean the Fourier series of a continuous-time periodic signal (or</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">a continuous-time function of finite scope), then no, Scilab doesn't do</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">that, because the
<span class="SpellE">FFT</span> is different from the Fourier Series.<span style="mso-spacerun:yes">
</span>If you have</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">a signal that's symbolically defined as f(t) over some span of time,</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">then Maxima may help you get a symbolic definition of the Fourier</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Series.</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">The
<span class="SpellE">FFT</span> is essentially the Fourier series of a sampled-time periodic (or</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">finite-scope) signal, so if that sampled-time signal is a sufficiently</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">accurate approximation of your continuous-time signal, and if your a0,</span></span></font></p>
<p class="MsoPlainText"><span class="SpellE"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">a_k</span></span></font></span> and
<span class="SpellE">b_k</span> are defined to match the way that Scilab does the
<span class="SpellE">FFT</span>, then</p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">the real part of the
<span class="SpellE">FFT</span> are the a coefficients, and the imaginary part</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">are the b coefficients.</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">If you gather up half a dozen books that include signal processing,</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">especially if some are from applications areas a bit removed from</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">"normal" signal processing, you'll find that everyone specifies their</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">Fourier stuff differently.<span style="mso-spacerun:yes">
</span>So what comes out of <span class="SpellE">Scilab's</span> <span class="SpellE">
FFT</span> may not</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">match _your_ definitions of a0, etc., but they match _someone's_.</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">On Thu, 2016-09-22 at 23:09 +0200,
<a href="mailto:paul.carrico@free.fr" target="_blank"><font color="black"><span style="color:windowtext;text-decoration:none;text-underline:none">paul.carrico@free.fr</span></font></a> wrote:</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> dear all</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">>
</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> I'm novice in Fourier series and other and my question is probably</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> naive (sorry for this) => I'm wondering if
<span class="SpellE">scilab</span> can directly</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> calculate the Fourier coefficient a0,
<span class="SpellE">a_k</span> and <span class="SpellE">b_k</span> ?</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">>
</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">>
</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> I'm currently doing it "by hand" is order to
<span class="SpellE">familiarise</span> myself with</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> it (and I'm looking at the same time to documents on<span style="mso-spacerun:yes">
</span><span class="SpellE">FFT</span> use and</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> rules to
<span class="SpellE">refind</span> the 2 natural frequencies of the example here bellow),</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> but it seems I'll need to code the coefficient calculations ... Am I</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> right ?</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">>
</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> Thanks</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">>
</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"><span style="font-size:11.0pt"><span style="mso-bidi-font-size:10.5pt">> Paul</span></span></font></p>
<p class="MsoPlainText"><font size="2" face="Calibri"> </font></p>
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