Image:Linearchirp.png

A graph of a sinusoidal linear chirp. It would be cool to show the f(t) function on the same graph. Any ideas?

[edit] Instructions

See Wikipedia graph-making tips.

Newest version created in Maxima using the command:

x(t):=sin(2*%PI*(.1+1*t)*t);

So f₀ = 0.1 Hz and k = 1, according to the equation given in the article:

x(t) = sin(2πf(t)t) = sin(2π(f₀ + kt)t)

It was then plotted using Maxima's gnuplot interface through the command:

plot2d(x(t),[t,0,5],[nticks,500], [gnuplot_preamble,"set grid x; set ytics 1; set yrange [-2:2]; set nokey"], [gnuplot_ps_term_command,"set term postscript enhanced landscape color solid lw 2 'Times-Roman' 20"], [gnuplot_term,ps], [gnuplot_out_file,"linchirp.ps"]);

To convert the PostScript file to PNG:

1. Open it in the GIMP (make sure you have ghostscript installed! - Windows instructions)
   • Enter 500 under Resolution (it doesn't say "DPI" but I think that's what it means)
   • Uncheck Try bounding box (since the bounding box cuts off the edge, unfortunately. You can try with the bounding box first.)
   • Enter large values for Width and Height
   • Check Color
   • Check Strong anti-aliasing for both graphics and text
2. Crop off extra whitespace (Shift+C if you can't find it in the toolbox)
3. Possibly need to rotate it: Click Image → Transform → Rotate 90 degrees clockwise
4. Filters → Blur → Gaussian blur at 2.0 px (No need to blur if you use strong anti-aliasing during conversion. I see no significant difference between end results.)
5. Image → Scale Image...
   • Width and Height at 25%
   • Cubic interpolation
6. You can view at normal size if you want by pressing 1, Ctrl+E
7. Save as Linearchirp.png

Created by User:Omegatron using gnuplot, possibly with post-processing in the GIMP (PNG) or Inkscape (SVG)

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• Chirp
• Chirp spread spectrum