File:Spektralzerlegung2.png
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[edit]DescriptionSpektralzerlegung2.png |
Deutsch: Die ersten 5 Schritte um einen Wienerprozess mit einer Fourierreihe darzustellen/konstruieren |
Source |
selbst erstellt mit GNU R. Der R-Quelltext: N<-20 steps<-300 cs<-rainbow(5) x=seq(from=0,to=1,length=steps) set.seed(303898) #S(t)=Z_0*t+sum sqrt(2)/(k*pi)*Z_k*sin(k*pi*t) Z=rnorm(N,mean=0,sd=1) Z0=rnorm(1,mean=0,sd=1) S=array(data=NA,dim=c(steps,N)) for (k in 1:N) { for (t in 1:steps) { sum=0 for (j in 1:k) { #aufsummieren sum=sum+sqrt(2)*sin(j*pi*t/steps)*Z[j]/(j*pi) } S[t,k]<-Z0*t/steps+sum } } png(filename = "Spektralzerlegung2.png", width=1500, height=1125) par(bg="lightgrey") plot(x,S[,1],type="l",xlab="",ylab="",ylim=c(min(S),max(S)),col=cs[1],lwd=3) lines(x,S[,2],col=cs[2],lwd=3) lines(x,S[,3],col=cs[3],lwd=3) lines(x,S[,4],col=cs[4],lwd=3) lines(x,S[,5],col=cs[5],lwd=3) legend(0.85,0.4,legend=c(1,2,3,4,5),lwd=6,col=cs,bg="grey",cex=1.6) title(main="Annäherung an einen Wienerprozess durch eine Fourierreihe",cex.main=3)dev.off() |
Author | Thomas Steiner |
Licensing
[edit]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 |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
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This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
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[edit]Transferred from de.wikipedia to Commons by Wdwdbot using script bot_filetrans.pl.
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current | 20:50, 9 October 2014 | 1,500 × 1,125 (20 KB) | Wdwdbot (talk | contribs) | Bot Move: Original uploader of this revision (#4) was Thire at de.wikipedia | |
20:50, 9 October 2014 | 1,500 × 1,125 (20 KB) | Wdwdbot (talk | contribs) | Bot Move: Original uploader of this revision (#3) was Thire at de.wikipedia | ||
20:49, 9 October 2014 | 1,500 × 1,125 (18 KB) | Wdwdbot (talk | contribs) | Bot Move: Original uploader of this revision (#2) was Thire at de.wikipedia | ||
20:49, 9 October 2014 | 893 × 569 (20 KB) | Wdwdbot (talk | contribs) | Bot Move: Original uploader of this revision (#1) was Benson.by at de.wikipedia |
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