Mathematica tool box 4

This is a short hands..on  introduction to Mathematica, part 4.

FOURIER TRANSFORM

({{"Fourier["{(Subscript["u", "1"])," "(Subscript["u", "2"])," … "","" "(Subscript["u", "n"])}"]"" ", "Fourier transform "}, {"InverseFourier["{(Subscript["v", "1"])," "(Subscript["v", "2"])," … "","" "(Subscript["v", "n"])}"]"" ", "inverse Fourier transform "}})

say you have an NMR signal that looks like this

data = Table[ N[Sin[30 2 Pi n/200] + (Random[ ] - 1/2)], {n, 200} ] ;

ListPlot[ data, PlotJoined -> True ]

and have FT

ListPlot[ Abs[Fourier[data]], PlotJoined -> True, PlotRange -> All ]

or  NMR  may be like this

data2 = Table[ N[100* Exp[-10( n/200)] Sin[30 2 Pi n/200] + (Random[ ] - 1/2)], {n, 200} ] ;

ListPlot[ data2, PlotJoined -> True, PlotRange->All ]

ListPlot[ Abs[Fourier[data2]], PlotJoined -> True, PlotRange -> All ]

Why are two signals?

What would be the signal if you have two different resonances combined?