File:XCubed Fourier Series Approximation n=7,15.svg

Description	XCubed Fourier Series Approximation n=7,15.svg This is a graph of x3, periodic on (-π,π), with the Fourier Series Approximations drawn in at k=7 (red) and k=15 (blue). The approximation is given by . This is the counterpart to this, which has just the original function drawn in.
Date	22 February 2008(2008-02-22)
Source	Own Drawing, Plotted in Mathematica, edited in Inkscape.
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Public domainPublic domainfalsefalse
Other versions	image:XCubed Periodic (-pi, pi).svg

[edit] Mathematica Code

f[x_] = x^3;

ffour[x_, k_] =
  Hold[
   Sum[
    ((-2*(-1)^n*(Pi^2*n^2 - 6))/(n^3))*Sin[n*x],
    {n, 1, k}]
   ];

Plot[
 {f[Mod[x, 2 \[Pi], -\[Pi]]],
  ReleaseHold[ffour[x, 7]],
  ReleaseHold[ffour[x, 15]]},
 {x, -2 Pi, 2 Pi}]

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	02:29, 23 February 2008		720 × 460 (83 KB)	Inductiveload	({{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }} )
	02:00, 23 February 2008		720 × 460 (83 KB)	Inductiveload	({{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }} )
	01:21, 10 February 2007		625 × 386 (189 KB)	Inductiveload	({{Information |Description=This is a graph of x<sup>3</sup>, periodic on (-π,π), with the Fourier Series Approximations drawn in at k=7 (red) and k=15 (blue). The approximation is given by <math>f\left( x \right) = \sum\limits_{n = 1}^k {{{ - 2\lef)

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• Signals and Systems/Fourier Series
• Signals and Systems/Print version

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