Mr. Parker (and anyone else with a long chunk of data to include in a post),

In the future, please try to place the data in a file that you attach to your post.
The file can be a Mathematica notebook or plain text, whichever is more convenient.

Having to scroll wa-a-a-a-a-ay down is inconvenient.

Moderation Team

Hello everybody,

thank you for all your answers. They made me think and I can tell you now more precise what I really need. Lets go back to my first post. There you can find my data (intensity vs. frequency). The frequency points are not spaced equally. They become closer to higher frequencies. This is why I can not use the FFT!!! This is were the problem begins.

This is my solution (if you have a better idea please tell me):

1. I'll try to interpolate my data (intensity vs. frequency). This data consist of N data points unequally spaced.
2. Then I arrange N equally spaced points over the interpolated function.
3. For this new points I can finally apply FFT. Doing so, I can then chop all the frequencies that I would like to get rid of.
4. Afterwards I use InverseFourier to get back to the frequency domain (intensity vs. frequency).
5. Then I transform my spectrum back from frequency domain to wavelength domain (intensity vs. wavelength).

I have to consider one very important fact: I have to make sure to not distort the data!!! This is important. I don't want to modify my data by accident.

If you have a better solution, let me please know!

I think I need your help to actually do all this.

Step one: First I tried it using InterpolatingPolynomial. This was not very succesfully. Then I tried this:

Result = FresnelFrequency1[[All, 2]];

n = Length[Result]; (*Number of y-values*)
ftres = FourierDCT[Result]; (*DFT*)
len = 80; (*Number of frequencies that I would like to consider*)
ftres = PadRight[Take[ftres, len], Length[Result], 0];
out = FourierDCT[ftres, 3];
fsum = 1/Sqrt[n]*(ftres[[1]] + 
     2*Sum[ftres[[r]]*Cos[Pi/n*(r - 1) (x - 1/2)], {r, 2, 
        Length[ftres]}]);

Show[Plot[fsum, {x, 0, 1000}, PlotRange -> All], 
 ListLinePlot[ Result,  PlotStyle -> Red]]

Problem here is, that the x-axis is not the same anymore. The function is plotted versus "pixel position" and not versus "frequency".

Step 2: I have an idea, but it is not exactly what I need. Assuming I know my underlying function. Let's simplify and say it is a sinus function. Then I will sample N data points over this function. Like here:

NumberOfPoints = 100;

Punkte = Table[Sin[{t}], {t, 0, NumberOfPoints}];
Punkte2 = Table[{t, Punkte[[t + 1, 1]]}, {t, 0, NumberOfPoints}];
Show[
 ListPlot[Punkte2],
 ListLinePlot[Punkte2]
 ]

But again, I change the x-axis. This is the problem.

Can you please help me solving this problem. Maybe somebody of you has a very beautiful solution or a much better idea in general.

Cheers,

Peter

What you're looking to do is de-trend your data. I haven't seen that done with a Fourier transform. I'm not sure how that'd work.

There are many different ways to detrend data. A really basic way to detrend is to use the EstimatedBackground function:

http://reference.wolfram.com/language/ref/EstimatedBackground.html

Once you find the background you can substract it from the signal to detrend it.

data[[All, 2]] - EstimatedBackground[data[[All, 2]], 20]