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File:Simple time domain vs frequency domain.svg

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English: Top:Example of a simple signal, comprised of two sine function. Bottom: The fourier-transformation if the same signal.
Deutsch: Oben: Ein einfaches Beispielsignal, bestehend aus zwei zusammenaddierten Sinusfunktionen.

Unten: Die Fouriertransformierte desselben Signals (vereinfachte Darstellung als kontinuierliche Linie).

Die Fouriertransformierte, wird häufig "im Frequenzraum" oder "das Frequenz-Spektrum" genannt. Für mathematische Zwecke ist es wichtig, die *digital* berechnete Fouriertransformation als solche zu kennzeichnen. Daher spricht man hier häufig bewusst auch von einer DFT oder eben FFT.
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Author Accountalive
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R code

f <- function(x)
{
  noise <- rnorm(1,0,0.05)
  a <-   sin(10*x)     
  b <-2*sin(   x)
  a+b
}

xr <- 20
res <- 10240

x <- seq(0,xr*2*pi,length.out=res)
y <- rep(0, length(x))
for( i in 0:length(x))
{
  y[i] <- f(x[i])
} 

ft <- abs(fft(y))

old.par <- par(mfrow=c(2, 1), yaxt="n", mgp=c(2,1,0), bty='l')

tToIndex = xr/res
tValues = ((1:length(y))-1) * tToIndex
plot(tValues,y,t='l', xlab="Zeit in s", ylab="signal",xlim=c(1,6),main="signal = 2 sin x  +  sin 10x ")

freqToIndex = xr
xvalues = ((1:length(ft))-1) / freqToIndex

plot(xvalues, ft,type='l'
     ,xlim=c(0,11), xlab='Frequenz in Hz', ylab="


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Example of a signal and its fourier-transformation, computed via FFT.

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22 April 2021

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Date/TimeThumbnailDimensionsUserComment
current08:58, 12 December 2022Thumbnail for version as of 08:58, 12 December 2022512 × 398 (30 KB)VectorVoyagerforgot to add "it" at line 104
08:57, 12 December 2022Thumbnail for version as of 08:57, 12 December 2022512 × 398 (30 KB)VectorVoyageradd Turkish and Italian
14:03, 22 April 2021Thumbnail for version as of 14:03, 22 April 2021512 × 398 (29 KB)AccountaliveFine tuning and translation via <switch>[https://commons.wikimedia.org/wiki/Commons:Translation_possible/Learn_more#Multiple_translations_within_one_SVG_file]
11:39, 22 April 2021Thumbnail for version as of 11:39, 22 April 2021778 × 603 (140 KB)AccountaliveUploaded own work with UploadWizard

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