Hello
I have a many data points (intensity vs. wavelength). The signal is noisy so I would like to smooth it. The signal is also sumperimposed with another sinusodial function which I try to get rid of. There are some steps where I need you help.
First, here is my long list of data:
Fresnel1 = {{1.549`, 0.004039`}, {1.549002`,
0.0044009999999999995`}, {1.549004`, 0.003989`}, {1.549006`,
0.004048`}, {1.5490080000000002`,
0.0039840000000000006`}, {1.54901`,
0.0038900000000000002`}, {1.549012`,
0.0037099999999999998`}, {1.549014`,
0.003989`}, {1.5490160000000002`, 0.003665`}, {1.549018`,
0.0035470000000000002`}, {1.54902`,
0.0035610000000000004`}, {1.549022`,
0.0036100000000000004`}, {1.549024`,
0.0033299999999999996`}, {1.549026`,
0.0036339999999999996`}, {1.549028`, 0.0037`}, {1.54903`,
0.003268`}, {1.549032`,
0.0033780000000000004`}, {1.5490340000000002`,
0.002851`}, {1.549036`, 0.002658`}, {1.5490380000000001`,
0.0028369999999999997`}, {1.54904`, 0.002932`}, {1.549042`,
0.0032370000000000003`}, {1.549044`,
0.002906`}, {1.5490460000000001`, 0.002509`}, {1.549048`,
0.002802`}, {1.54905`,
0.0030050000000000003`}, {1.5490519999999999`,
0.002907`}, {1.5490540000000002`, 0.002761`}, {1.549056`,
0.002904`}, {1.549058`,
0.0025680000000000004`}, {1.5490599999999999`,
0.0028970000000000003`}, {1.549062`,
0.002852`}, {1.5490640000000002`,
0.0032010000000000003`}, {1.549066`,
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0.00326`}, {1.54907`, 0.0034210000000000004`}, {1.549072`,
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0.0036339999999999996`}, {1.549078`,
0.0035499999999999998`}, {1.54908`,
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0.003939`}, {1.5490840000000001`, 0.003859`}, {1.549086`,
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As you can see the data is quite noisy and the signal is superimposed with another sinus:
Show[
ListPlot[Fresnel1, AxesLabel -> {"wavelength [\[Mu]m]", "Intensity"}],
ListLinePlot[Fresnel1, PlotStyle -> {Thin, PointSize[0.1]},
AxesLabel -> {"wavelength [\[Mu]m]", "Intensity"}]
]
What I want to do is:
1.) Filter the sinus with smaller frequency out of my signal
2.) Smooth my signal by filtering the noise
As far as I understand the FFT I have to convert my signal from wavelength into frequency. Then I can apply the Mathematica functions Fourier[] and InverseFourier[] to filter my signal. But I think there is one important think to keep in mind and this is why I need your help.
If I convert the wavelength signal to frequency, the step size changes (is not equal anymore: delta lambda compared to delta frequency). And I have heard that this is important. First of all, is this actually correct? If yes, can you explain me why or where I can find more information about it? I think I have to define a wavelength array. How does this look like?
Fi = First[Dimensions [Fresnel1]];
FresnelFrequency1 =
Table[{(3*10^8)/Fresnel1[[t, 1]]*10^6, Fresnel1[[t, 2]]}, {t,
Fi}];
Show[
ListPlot[FresnelFrequency1,
AxesLabel -> {"Frequency [Hz]", "Intensity"}],
ListLinePlot[FresnelFrequency1, PlotStyle -> {Thin, PointSize[0.1]},
AxesLabel -> {"Frequency [Hz]", "Intensity"}]
]
Because I think I have to deal with this sort of problem more often in the future, how would you solve step (1) and step (2) ?
Hope you can help me.
Peter