Image:Exponentialchirp.png

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A graph of a sinusoidal exponential 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)*(3^t)*t);

So f₀ = 0.1 Hz, and k = 3, according to the equation given in the article:

x (t) = sin(2π f (t) t) = sin(2π f 0 k t 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,"logchirp.ps"]);

To convert the PostScript file to PNG:

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
Crop off extra whitespace (Shift+C if you can't find it in the toolbox)
Possibly need to rotate it: Click Image → Transform → Rotate 90 degrees clockwise
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.)
Image → Scale Image...
- Width and Height at 25%
- Cubic interpolation
You can view at normal size if you want by pressing 1, Ctrl+E
Save as Exponentialchirp.png

(There were some artifacts of the lines being "painted with a pointy brush" in the high frequency section, so I just clipped off the tops with the GIMP brush.)

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

I, the author of this work, hereby publish it under the following licenses:

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".