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' The frames of the animation can be drawn
' by the code below in BASIC. The animation
' is made by collecting the frames in an
' image editor such as GIMP.
REM Constant
pi=4*atn(1)
REM Set up plotting area
screen 12
window (0,-2)-(5*pi,2)
REM Number of terms to use
for nt=1 to 25
cls
print "Harmonics:";nt
REM Plot squarewave
pset (0,0)
for w=0 to 5*pi step .01
line -(w,sgn(sin(w))),4
next w
REM Plot sum of terms
pset (0,0)
for w=0 to 5*pi step .01
y=0
for k=1 to nt
y=y+sin((2*k-1)*w)/(2*k-1)
next k
y=4*y/pi
line -(w,y)
next w
REM Freeze display (create a gif animation frame)
delay .2
next nt
Summary
Additive synthesis of a square wave, illustrating Fourier series expansion and Gibbs phenomenon.
See also: Image:Synthesis sawtooth.gif, Image:Synthesis triangle.gif
Licensing
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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. http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue
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File usage
The following pages on Schools Wikipedia link to this image (list may be incomplete):