File:Analytic.svg

Summary

Description A signal and the magnitude of its analytic signal, to demonstrate the envelope effect. I made it using Octave (that uses Gnuplot internally to output in SVG).
Date
Source Image:Analytic.png
Author original work by User:Omegatron, adapted to SVG by Alessio Damato
Other versions
SVG development
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Source code
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Python code

Python source code
from numpy import arange, sin, pi
from scipy.signal import hilbert
import matplotlib.pyplot as plt
plt.rc('svg', fonttype='none')

dt = 1e-3
t = arange(dt, 3, dt)
y1 = -(1.2 / t) - t + 3
y1[y1 < 0] = 0
y2 = sin(2 * 3 * pi * t)
y3 = y1 * y2
y4 = abs(hilbert(y3))

fig, ax = plt.subplots(1,1,figsize=(8,5))
ax.plot(t, y3, color='blue')
ax.plot(t, y4, color='red')
ax.grid(True)
ax.minorticks_on()
ax.set_xlim([0,3])
ax.set_xlabel(r'$t$')
ax.set_ylabel(r'$y$')
fig.savefig('analytic.svg', bbox_inches='tight')

Data

Matlab source code
t=[0:.0001:3]; 
y1=-(1.2./t)-t+3;  
y1(y1<0)=0;
y2=sin(2*3*pi*t);
y3=y1.*y2;
hil=abs(hilbert(y3));

gset terminal svg enhanced fname "Times" fsize 20
gset output "analytic.svg"                                          
gset nokey                                                         
gset yrange [-1:1]                                                 

plot(t,y3,"3",t,hil,"1");

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
Category:License migration redundant#Analytic.svgCategory:GFDL#Analytic.svg
w:en:Creative Commons
attribution share alike		 This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
This licensing tag was added to this file as part of the GFDL licensing update.
Category:CC-BY-SA-3.0-migrated#Analytic.svg
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic, 2.0 Generic and 1.0 Generic license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Category:CC-BY-SA-2.5,2.0,1.0#Analytic.svg
You may select the license of your choice.
Category:Self-published work Category:Images with Octave source code Category:Envelopes (signal) Category:Modulation Category:Signal processing
Category:CC-BY-SA-2.5,2.0,1.0 Category:CC-BY-SA-3.0-migrated Category:Envelopes (signal) Category:GFDL Category:Images with Octave source code Category:License migration redundant Category:Modulation Category:Self-published work Category:Signal processing Category:Valid SVG created with Matplotlib code