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--></style></head><body lang=EN-US link=blue vlink="#954F72"><div class=WordSection1><p class=MsoNormal>Claus,</p><p class=MsoNormal>Back in the late 60s, I did my PhD research using analytic signal. Yes,it works, and the implementation details are more complex that we find on the link. A few years ago, I implemented a system for analyzing harbor porpoise vocalizations using scilab. For example, instantaneous phase(t) wants to be differentiable if instantaneous frequency is to be positive. I found that octave bands are the widest that preserves this feature. Yes, you can calculate phase(t) = atan(imaginary/real), but you have to add 2PI when atan wraps around in order to make phase monotonically increase.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Also, I am not convinced that a loudspeaker does phase modulation. Certainly, if the speaker is linear, then superposition applies. If phase modulation occurs, it is a non-linear effect. Perhaps that effect is real, but we need to see a model to show how it comes to be. </p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I might be able to help you write analytic signal code. </p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Good wishes</p><p class=MsoNormal>Gary Nelson </p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Sent from my Windows 10 phone</p><p class=MsoNormal><o:p> </o:p></p><div style='mso-element:para-border-div;border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='border:none;padding:0in'><b>From: </b><a href="mailto:cfuttrup@gmail.com">Claus Futtrup</a><br><b>Sent: </b>Saturday, May 26, 2018 7:41 AM<br><b>To: </b><a href="mailto:users@lists.scilab.org">International users mailing list for Scilab.</a><br><b>Subject: </b>Re: [Scilab-users] Simulating phase modulation</p></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>Hi Rafael</p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Thank you, I shall print and study. :-)</p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Cheers,</p></div><div><p class=MsoNormal>Claus</p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Fri, May 25, 2018 at 8:42 PM Rafael Guerra <<a href="mailto:jrafaelbguerra@hotmail.com">jrafaelbguerra@hotmail.com</a>> wrote:</p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Hi Claus,</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>I am not aware of such function. However, you can find simple code here below for both phase modulation and demodulation, which is straightforward to translate in Scilab:</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'><a href="https://www.gaussianwaves.com/2017/06/phase-demodulation-using-hilbert-transform-application-of-analytic-signal/" target="_blank">https://www.gaussianwaves.com/2017/06/phase-demodulation-using-hilbert-transform-application-of-analytic-signal/</a></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Note that the phase modulation is coded differently from you snippet below.</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Regards,</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Rafael</span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>From:</b> users [mailto:<a href="mailto:users-bounces@lists.scilab.org" target="_blank">users-bounces@lists.scilab.org</a>] <b>On Behalf Of </b>Claus Futtrup<br><b>Sent:</b> Friday, May 25, 2018 7:17 PM<br><b>To:</b> International users mailing list for Scilab. <<a href="mailto:users@lists.scilab.org" target="_blank">users@lists.scilab.org</a>><br><b>Subject:</b> [Scilab-users] Simulating phase modulation</p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Hi there</p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>In a loudspeaker the driver can move several <span class=m-860483954252869115gmail-ginger-module-highlighter-mistake-anim>millimeter</span> in an attempt to reproduce a low-frequency note. If the speaker also at the same time produce a higher tone, this second tone is phase modulated by the first one. This is a distortion of the original signal which I'd like to simulate / illustrate with some simple Scilab code, if possible.</p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>In Matlab this can be simulated with <span class=m-860483954252869115gmail-ginger-module-highlighter-mistake-anim>pmmod</span>.</p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="https://matlabandsimulink.wordpress.com/2013/03/12/phase-modulation/" target="_blank">https://matlabandsimulink.wordpress.com/2013/03/12/phase-modulation/</a></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Is there a similar function in Scilab? (name - please ?)</p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Here's the code I have written so far - this is the part that shows the input signal (the un-distorted signal):</p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p></div><div><pre><span style='font-family:"Monospaced",serif;color:black'>sample_rate</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>=</span><span style='font-family:"Monospaced",serif;color:rosybrown'>20000</span><span style='font-family:"Monospaced",serif;color:black'>;</span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>t</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:rosybrown'>0</span><span style='color:#FFAA00'>:</span><span style='color:rosybrown'>1</span><span style='color:#5C5C5C'>/</span><span style='color:black'>sample_rate</span><span style='color:#FFAA00'>:</span><span style='color:rosybrown'>0.6</span><span style='color:black'>;</span></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>N</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>=</span><span style='font-family:"Monospaced",serif;color:#32B9B9'>size</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:black'>t,</span><span style='font-family:"Monospaced",serif;color:rosybrown'>'*'</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>;</span><span style='font-family:"Monospaced",serif'> <i><span style='color:#64AE64'>//number of samples</span></i></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>y1</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:#32B9B9'>sin</span><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>2</span><span style='color:#5C5C5C'>*</span><span style='color:orchid'>%pi</span><span style='color:#5C5C5C'>*</span><span style='color:rosybrown'>50</span><span style='color:#5C5C5C'>*</span><span style='color:black'>t</span><span style='color:#4A55DB'>)</span><span style='color:black'>;</span></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>y2</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:rosybrown'>0.5</span><span style='color:#5C5C5C'>*</span><span style='color:#32B9B9'>sin</span><span style='color:#4A55DB'>(</span><span style='color:rosybrown'>2</span><span style='color:#5C5C5C'>*</span><span style='color:orchid'>%pi</span><span style='color:#5C5C5C'>*</span><span style='color:rosybrown'>500</span><span style='color:#5C5C5C'>*</span><span style='color:black'>t</span><span style='color:#4A55DB'>)</span><span style='color:black'>;</span></span></pre><pre><i><span style='font-family:"Monospaced",serif;color:#64AE64'>// y2 = 0.5*sin(2*%pi*500*t+%pi/4);</span></i></pre><pre><span style='font-family:"Monospaced",serif;color:black'>s</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>=</span><span style='font-family:"Monospaced",serif;color:black'>y1</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>+</span><span style='font-family:"Monospaced",serif;color:black'>y2</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>+</span><span style='font-family:"Monospaced",serif;color:#32B9B9'>grand</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>1</span><span style='font-family:"Monospaced",serif;color:black'>,N,</span><span style='font-family:"Monospaced",serif;color:rosybrown'>'nor'</span><span style='font-family:"Monospaced",serif;color:black'>,</span><span style='font-family:"Monospaced",serif;color:rosybrown'>0</span><span style='font-family:"Monospaced",serif;color:black'>,</span><span style='font-family:"Monospaced",serif;color:rosybrown'>1</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>;</span></pre><pre><span style='font-family:"Monospaced",serif'> </span></pre><pre><i><span style='font-family:"Monospaced",serif;color:#64AE64'>// Plot time-domain</span></i></pre><pre><span style='font-family:"Monospaced",serif;color:black'>endplot</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:#32B9B9'>round</span><span style='color:#4A55DB'>(</span><span style='color:black'>N</span><span style='color:#5C5C5C'>/</span><span style='color:rosybrown'>15</span><span style='color:#4A55DB'>)</span><span style='color:black'>;</span></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>twoplots</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:black'>scf</span><span style='color:#4A55DB'>()</span><span style='color:black'>;</span> <i><span style='color:#64AE64'>// Set Current Figure (Graphics Window)</span></i></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>subplot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>211</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>;</span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>plot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:black'>t</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>1</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:</span><span style='font-family:"Monospaced",serif;color:black'>endplot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>,y1</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>1</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:</span><span style='font-family:"Monospaced",serif;color:black'>endplot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>,t</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>1</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:</span><span style='font-family:"Monospaced",serif;color:black'>endplot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>,y2</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>1</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:</span><span style='font-family:"Monospaced",serif;color:black'>endplot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>))</span><span style='font-family:"Monospaced",serif;color:black'>;</span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>subplot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>212</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>;</span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>plot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:black'>t</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>1</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:</span><span style='font-family:"Monospaced",serif;color:black'>endplot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>,y1</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>1</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:</span><span style='font-family:"Monospaced",serif;color:black'>endplot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>+</span><span style='font-family:"Monospaced",serif;color:black'>y2</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>1</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:</span><span style='font-family:"Monospaced",serif;color:black'>endplot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>))</span><span style='font-family:"Monospaced",serif;color:black'>;</span></pre><pre><span style='font-family:"Monospaced",serif'> </span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>y</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>=</span><span style='font-family:"Monospaced",serif;color:#32B9B9'>fft</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:black'>s</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>;</span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>ymax</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:#32B9B9'>max</span><span style='color:#4A55DB'>(</span><span style='color:#32B9B9'>abs</span><span style='color:#4A55DB'>(</span><span style='color:black'>y</span><span style='color:#4A55DB'>))</span><span style='color:black'>;</span></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>y</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:black'>y</span> <span style='color:#5C5C5C'>./</span> <span style='color:black'>ymax;</span> <i><span style='color:#64AE64'>// Normalize</span></i></span></pre><pre><span style='font-family:"Monospaced",serif'> </span></pre><pre><i><span style='font-family:"Monospaced",serif;color:#64AE64'>// s is real so the fft response is conjugate symmetric</span></i></pre><pre><i><span style='font-family:"Monospaced",serif;color:#64AE64'>// and we retain only the first N/2 points</span></i></pre><pre><span style='font-family:"Monospaced",serif;color:black'>f</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>=</span><span style='font-family:"Monospaced",serif;color:black'>sample_rate</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>*</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>0</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:black'>N</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>/</span><span style='font-family:"Monospaced",serif;color:rosybrown'>2</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>))</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>/</span><span style='font-family:"Monospaced",serif;color:black'>N;</span><span style='font-family:"Monospaced",serif'> <i><span style='color:#64AE64'>//associated frequency vector</span></i></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>n</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>=</span><span style='font-family:"Monospaced",serif;color:#32B9B9'>size</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:black'>f,</span><span style='font-family:"Monospaced",serif;color:rosybrown'>'*'</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>;</span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>fftplots</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:black'>scf</span><span style='color:#4A55DB'>()</span><span style='color:black'>;</span></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>plot</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:black'>f</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>2</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:$</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)</span><span style='font-family:"Monospaced",serif;color:black'>,</span><span style='font-family:"Monospaced",serif;color:#32B9B9'>abs</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:black'>y</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>(</span><span style='font-family:"Monospaced",serif;color:rosybrown'>2</span><span style='font-family:"Monospaced",serif;color:#FFAA00'>:</span><span style='font-family:"Monospaced",serif;color:black'>n</span><span style='font-family:"Monospaced",serif;color:#4A55DB'>)))</span><span style='font-family:"Monospaced",serif;color:black'>;</span><span style='font-family:"Monospaced",serif'> <i><span style='color:#64AE64'>// drop first datapoint, f = 0 (it prevents log-plot)</span></i></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>a</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:black'>gca</span><span style='color:#4A55DB'>()</span><span style='color:black'>;</span></span></pre><pre><span style='font-family:"Monospaced",serif;color:black'>a</span><span style='font-family:"Monospaced",serif;color:#5C5C5C'>.</span><span style='font-family:"Monospaced",serif;color:#AAAAAA'>log_flags</span><span style='font-family:"Monospaced",serif'> <span style='color:#5C5C5C'>=</span> <span style='color:rosybrown'>"lnn"</span><span style='color:black'>;</span></span></pre><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> </p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Best regards,</p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Claus</p></div></div></div></div></blockquote></div><p class=MsoNormal style='margin-left:4.8pt'>_______________________________________________<br>users mailing list<br><a href="mailto:users@lists.scilab.org" target="_blank">users@lists.scilab.org</a><br><a href="http://lists.scilab.org/mailman/listinfo/users" target="_blank">http://lists.scilab.org/mailman/listinfo/users</a></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>