[Scilab-users] Simulating phase modulation

[Gary Nelson]

Claus,
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.

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. 

I might be able to help you write analytic signal  code. 

Good wishes
Gary Nelson 


Sent from my Windows 10 phone

From: Claus Futtrup
Sent: Saturday, May 26, 2018 7:41 AM
To: International users mailing list for Scilab.
Subject: Re: [Scilab-users] Simulating phase modulation

Hi Rafael

Thank you, I shall print and study. :-)

Cheers,
Claus

On Fri, May 25, 2018 at 8:42 PM Rafael Guerra <jrafaelbguerra at hotmail.com> wrote:
Hi Claus,
 
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:
https://www.gaussianwaves.com/2017/06/phase-demodulation-using-hilbert-transform-application-of-analytic-signal/
 
Note that the phase modulation is coded differently from you snippet below.
 
Regards,
Rafael
 
From: users [mailto:users-bounces at lists.scilab.org] On Behalf Of Claus Futtrup
Sent: Friday, May 25, 2018 7:17 PM
To: International users mailing list for Scilab. <users at lists.scilab.org>
Subject: [Scilab-users] Simulating phase modulation
 
Hi there
 
In a loudspeaker the driver can move several millimeter 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.
 
In Matlab this can be simulated with pmmod.
https://matlabandsimulink.wordpress.com/2013/03/12/phase-modulation/
 
Is there a similar function in Scilab? (name - please ?)
 
Here's the code I have written so far - this is the part that shows the input signal (the un-distorted signal):
 
sample_rate=20000;
t = 0:1/sample_rate:0.6;
N=size(t,'*'); //number of samples
y1 = sin(2*%pi*50*t);
y2 = 0.5*sin(2*%pi*500*t);
// y2 = 0.5*sin(2*%pi*500*t+%pi/4);
s=y1+y2+grand(1,N,'nor',0,1);
 
// Plot time-domain
endplot = round(N/15);
twoplots = scf(); // Set Current Figure (Graphics Window)
subplot(211);
plot(t(1:endplot),y1(1:endplot),t(1:endplot),y2(1:endplot));
subplot(212);
plot(t(1:endplot),y1(1:endplot)+y2(1:endplot));
 
y=fft(s);
ymax = max(abs(y));
y = y ./ ymax; // Normalize
 
// s is real so the fft response is conjugate symmetric
// and we retain only the first N/2 points
f=sample_rate*(0:(N/2))/N; //associated frequency vector
n=size(f,'*');
fftplots = scf();
plot(f(2:$),abs(y(2:n))); // drop first datapoint, f = 0 (it prevents log-plot)
a = gca();
a.log_flags = "lnn";
 
Best regards,
Claus
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