2 added 12413 characters in body

EDIT

Thanks for the replies. I forgot to mention that data is equally spaced in time (in 300 bins).

First column is time in seconds and second column are photons counts. Notice that the absolute values of time are not (scientifically) relevant because in the end I will compare the Fourier results of this light curve (obtained in one energy band) with the results obtained on different curves in other energy bands and I am interested in the delays among them.

Also, if relevant, I would analyze these curves in a positive frequency range (10^5-10^2 Hz). I am studying more about Fourier transformation and its definition on Mathematica in the links you shared, thank you!

Here is the data:

 0.3450333333E+01               0
0.1035100000E+02               0
0.1725166667E+02               0
0.2415233333E+02               0
0.3105300000E+02               0
0.3795366667E+02               0
0.4485433333E+02               0
0.5175500000E+02               0
0.5865566666E+02               0
0.6555633333E+02               0
0.7245699999E+02               0
0.7935766666E+02               0
0.8625833332E+02               1
0.9315900000E+02               0
0.1000596667E+03               0
0.1069603333E+03               0
0.1138610000E+03               0
0.1207616666E+03               0
0.1276623334E+03               0
0.1345630000E+03               0
0.1414636666E+03               0
0.1483643333E+03               0
0.1552650000E+03               0
0.1621656666E+03               0
0.1690663334E+03               0
0.1759670000E+03               0
0.1828676666E+03               0
0.1897683334E+03               0
0.1966690000E+03               0
0.2035696666E+03               0
0.2104703334E+03               0
0.2173710000E+03               0
0.2242716666E+03               0
0.2311723334E+03               0
0.2380730000E+03               0
0.2449736666E+03               0
0.2518743334E+03               0
0.2587750000E+03               0
0.2656756666E+03               0
0.2725763333E+03               0
0.2794769999E+03               0
0.2863776666E+03               0
0.2932783333E+03               0
0.3001789999E+03               0
0.3070796666E+03               0
0.3139803333E+03               1
0.3208809999E+03               0
0.3277816667E+03               0
0.3346823333E+03               0
0.3415829999E+03               1
0.3484836667E+03               1
0.3553843333E+03               0
0.3622849999E+03               1
0.3691856667E+03               0
0.3760863333E+03               0
0.3829869999E+03               1
0.3898876667E+03               0
0.3967883333E+03               0
0.4036889999E+03               1
0.4105896667E+03               1
0.4174903333E+03               3
0.4243909999E+03               0
0.4312916667E+03               0
0.4381923333E+03               0
0.4450929999E+03               0
0.4519936667E+03               0
0.4588943333E+03               1
0.4657950000E+03               0
0.4726956667E+03               0
0.4795963333E+03               2
0.4864970000E+03               1
0.4933976667E+03               0
0.5002983333E+03               0
0.5071990000E+03               0
0.5140996667E+03               1
0.5210003333E+03               0
0.5279009999E+03               1
0.5348016667E+03               0
0.5417023333E+03               0
0.5486029999E+03               0
0.5555036667E+03               0
0.5624043333E+03               0
0.5693049999E+03               0
0.5762056667E+03               1
0.5831063333E+03               0
0.5900069999E+03               0
0.5969076667E+03               1
0.6038083333E+03               3
0.6107089999E+03               4
0.6176096667E+03               1
0.6245103333E+03               1
0.6314109999E+03               0
0.6383116667E+03               0
0.6452123333E+03               1
0.6521129999E+03               2
0.6590136667E+03               2
0.6659143333E+03               3
0.6728149999E+03               3
0.6797156667E+03               5
0.6866163333E+03               6
0.6935169999E+03               7
0.7004176667E+03               4
0.7073183333E+03               5
0.7142189999E+03               4
0.7211196666E+03               6
0.7280203333E+03              11
0.7349209999E+03               5
0.7418216666E+03               4
0.7487223333E+03               3
0.7556229999E+03               8
0.7625236666E+03               6
0.7694243333E+03               8
0.7763250000E+03               5
0.7832256666E+03              14
0.7901263333E+03             111
0.7970270000E+03             387
0.8039276666E+03             682
0.8108283333E+03            1120
0.8177290000E+03            1461
0.8246296666E+03            1788
0.8315303333E+03            1985
0.8384310000E+03            2167
0.8453316666E+03            2308
0.8522323333E+03            2394
0.8591329999E+03            2447
0.8660336666E+03            2465
0.8729343333E+03            2503
0.8798349999E+03            2629
0.8867356666E+03            2629
0.8936363333E+03            2566
0.9005369999E+03            2518
0.9074376666E+03            2519
0.9143383333E+03            2498
0.9212390000E+03            2513
0.9281396666E+03            2380
0.9350403333E+03            2548
0.9419410000E+03            2368
0.9488416666E+03            2366
0.9557423333E+03            2317
0.9626430000E+03            2386
0.9695436666E+03            2383
0.9764443332E+03            2404
0.9833450000E+03            2222
0.9902456666E+03            2355
0.9971463334E+03            2160
0.1004047000E+04            2292
0.1010947666E+04            2112
0.1017848334E+04            2116
0.1024749000E+04            2098
0.1031649666E+04            2060
0.1038550333E+04            2101
0.1045451000E+04            1941
0.1052351666E+04            1989
0.1059252334E+04            1848
0.1066153000E+04            1819
0.1073053666E+04            1740
0.1079954333E+04            1643
0.1086855000E+04            1635
0.1093755666E+04            1583
0.1100656334E+04            1511
0.1107557000E+04            1510
0.1114457666E+04            1436
0.1121358333E+04            1289
0.1128259000E+04            1238
0.1135159666E+04            1263
0.1142060334E+04            1183
0.1148961000E+04            1124
0.1155861666E+04            1055
0.1162762333E+04             996
0.1169663000E+04             956
0.1176563666E+04             965
0.1183464334E+04             818
0.1190365000E+04             835
0.1197265666E+04             801
0.1204166333E+04             735
0.1211067000E+04             698
0.1217967666E+04             619
0.1224868334E+04             631
0.1231769000E+04             624
0.1238669666E+04             522
0.1245570333E+04             515
0.1252471000E+04             503
0.1259371666E+04             501
0.1266272334E+04             500
0.1273173000E+04             463
0.1280073666E+04             440
0.1286974333E+04             418
0.1293875000E+04             407
0.1300775667E+04             384
0.1307676334E+04             374
0.1314577000E+04             359
0.1321477666E+04             359
0.1328378334E+04             326
0.1335279000E+04             288
0.1342179667E+04             259
0.1349080334E+04             226
0.1355981000E+04             214
0.1362881666E+04             173
0.1369782334E+04             144
0.1376683000E+04             121
0.1383583667E+04             139
0.1390484334E+04             106
0.1397385000E+04             100
0.1404285666E+04              70
0.1411186334E+04              63
0.1418087000E+04              52
0.1424987667E+04              50
0.1431888334E+04              51
0.1438789000E+04              39
0.1445689666E+04              44
0.1452590334E+04              30
0.1459491000E+04              42
0.1466391667E+04              19
0.1473292334E+04              25
0.1480193000E+04              17
0.1487093666E+04              28
0.1493994334E+04              17
0.1500895000E+04              13
0.1507795667E+04              14
0.1514696334E+04               9
0.1521597000E+04               7
0.1528497666E+04               4
0.1535398334E+04               1
0.1542299000E+04               7
0.1549199667E+04               8
0.1556100334E+04               1
0.1563001000E+04               6
0.1569901666E+04               6
0.1576802334E+04               2
0.1583703000E+04               0
0.1590603667E+04               1
0.1597504334E+04               3
0.1604405000E+04               1
0.1611305666E+04               1
0.1618206334E+04               0
0.1625107000E+04               2
0.1632007667E+04               1
0.1638908334E+04               1
0.1645809000E+04               1
0.1652709666E+04               1
0.1659610334E+04               0
0.1666511000E+04               0
0.1673411667E+04               1
0.1680312334E+04               1
0.1687213000E+04               0
0.1694113666E+04               0
0.1701014334E+04               0
0.1707915000E+04               0
0.1714815667E+04               0
0.1721716334E+04               0
0.1728617000E+04               0
0.1735517666E+04               0
0.1742418334E+04               0
0.1749319000E+04               0
0.1756219667E+04               0
0.1763120334E+04               0
0.1770021000E+04               0
0.1776921666E+04               0
0.1783822334E+04               0
0.1790723000E+04               0
0.1797623667E+04               0
0.1804524334E+04               0
0.1811425000E+04               0
0.1818325666E+04               0
0.1825226334E+04               0
0.1832127000E+04               0
0.1839027667E+04               0
0.1845928334E+04               0
0.1852829000E+04               0
0.1859729666E+04               0
0.1866630334E+04               0
0.1873531000E+04               0
0.1880431667E+04               0
0.1887332334E+04               0
0.1894233000E+04               0
0.1901133666E+04               0
0.1908034334E+04               0
0.1914935000E+04               0
0.1921835667E+04               0
0.1928736334E+04               0
0.1935637000E+04               0
0.1942537666E+04               0
0.1949438333E+04               0
0.1956339000E+04               0
0.1963239667E+04               0
0.1970140333E+04               0
0.1977041000E+04               0
0.1983941666E+04               0
0.1990842333E+04               0
0.1997743000E+04               0
0.2004643667E+04               0
0.2011544333E+04               0
0.2018445000E+04               0
0.2025345666E+04               0
0.2032246333E+04               0
0.2039147000E+04               0
0.2046047667E+04               0
0.2052948333E+04               0
0.2059849000E+04               0
0.2066749666E+04               0


EDIT

Thanks for the replies. I forgot to mention that data is equally spaced in time (in 300 bins).

First column is time in seconds and second column are photons counts. Notice that the absolute values of time are not (scientifically) relevant because in the end I will compare the Fourier results of this light curve (obtained in one energy band) with the results obtained on different curves in other energy bands and I am interested in the delays among them.

Also, if relevant, I would analyze these curves in a positive frequency range (10^5-10^2 Hz). I am studying more about Fourier transformation and its definition on Mathematica in the links you shared, thank you!

Here is the data:

 0.3450333333E+01               0
0.1035100000E+02               0
0.1725166667E+02               0
0.2415233333E+02               0
0.3105300000E+02               0
0.3795366667E+02               0
0.4485433333E+02               0
0.5175500000E+02               0
0.5865566666E+02               0
0.6555633333E+02               0
0.7245699999E+02               0
0.7935766666E+02               0
0.8625833332E+02               1
0.9315900000E+02               0
0.1000596667E+03               0
0.1069603333E+03               0
0.1138610000E+03               0
0.1207616666E+03               0
0.1276623334E+03               0
0.1345630000E+03               0
0.1414636666E+03               0
0.1483643333E+03               0
0.1552650000E+03               0
0.1621656666E+03               0
0.1690663334E+03               0
0.1759670000E+03               0
0.1828676666E+03               0
0.1897683334E+03               0
0.1966690000E+03               0
0.2035696666E+03               0
0.2104703334E+03               0
0.2173710000E+03               0
0.2242716666E+03               0
0.2311723334E+03               0
0.2380730000E+03               0
0.2449736666E+03               0
0.2518743334E+03               0
0.2587750000E+03               0
0.2656756666E+03               0
0.2725763333E+03               0
0.2794769999E+03               0
0.2863776666E+03               0
0.2932783333E+03               0
0.3001789999E+03               0
0.3070796666E+03               0
0.3139803333E+03               1
0.3208809999E+03               0
0.3277816667E+03               0
0.3346823333E+03               0
0.3415829999E+03               1
0.3484836667E+03               1
0.3553843333E+03               0
0.3622849999E+03               1
0.3691856667E+03               0
0.3760863333E+03               0
0.3829869999E+03               1
0.3898876667E+03               0
0.3967883333E+03               0
0.4036889999E+03               1
0.4105896667E+03               1
0.4174903333E+03               3
0.4243909999E+03               0
0.4312916667E+03               0
0.4381923333E+03               0
0.4450929999E+03               0
0.4519936667E+03               0
0.4588943333E+03               1
0.4657950000E+03               0
0.4726956667E+03               0
0.4795963333E+03               2
0.4864970000E+03               1
0.4933976667E+03               0
0.5002983333E+03               0
0.5071990000E+03               0
0.5140996667E+03               1
0.5210003333E+03               0
0.5279009999E+03               1
0.5348016667E+03               0
0.5417023333E+03               0
0.5486029999E+03               0
0.5555036667E+03               0
0.5624043333E+03               0
0.5693049999E+03               0
0.5762056667E+03               1
0.5831063333E+03               0
0.5900069999E+03               0
0.5969076667E+03               1
0.6038083333E+03               3
0.6107089999E+03               4
0.6176096667E+03               1
0.6245103333E+03               1
0.6314109999E+03               0
0.6383116667E+03               0
0.6452123333E+03               1
0.6521129999E+03               2
0.6590136667E+03               2
0.6659143333E+03               3
0.6728149999E+03               3
0.6797156667E+03               5
0.6866163333E+03               6
0.6935169999E+03               7
0.7004176667E+03               4
0.7073183333E+03               5
0.7142189999E+03               4
0.7211196666E+03               6
0.7280203333E+03              11
0.7349209999E+03               5
0.7418216666E+03               4
0.7487223333E+03               3
0.7556229999E+03               8
0.7625236666E+03               6
0.7694243333E+03               8
0.7763250000E+03               5
0.7832256666E+03              14
0.7901263333E+03             111
0.7970270000E+03             387
0.8039276666E+03             682
0.8108283333E+03            1120
0.8177290000E+03            1461
0.8246296666E+03            1788
0.8315303333E+03            1985
0.8384310000E+03            2167
0.8453316666E+03            2308
0.8522323333E+03            2394
0.8591329999E+03            2447
0.8660336666E+03            2465
0.8729343333E+03            2503
0.8798349999E+03            2629
0.8867356666E+03            2629
0.8936363333E+03            2566
0.9005369999E+03            2518
0.9074376666E+03            2519
0.9143383333E+03            2498
0.9212390000E+03            2513
0.9281396666E+03            2380
0.9350403333E+03            2548
0.9419410000E+03            2368
0.9488416666E+03            2366
0.9557423333E+03            2317
0.9626430000E+03            2386
0.9695436666E+03            2383
0.9764443332E+03            2404
0.9833450000E+03            2222
0.9902456666E+03            2355
0.9971463334E+03            2160
0.1004047000E+04            2292
0.1010947666E+04            2112
0.1017848334E+04            2116
0.1024749000E+04            2098
0.1031649666E+04            2060
0.1038550333E+04            2101
0.1045451000E+04            1941
0.1052351666E+04            1989
0.1059252334E+04            1848
0.1066153000E+04            1819
0.1073053666E+04            1740
0.1079954333E+04            1643
0.1086855000E+04            1635
0.1093755666E+04            1583
0.1100656334E+04            1511
0.1107557000E+04            1510
0.1114457666E+04            1436
0.1121358333E+04            1289
0.1128259000E+04            1238
0.1135159666E+04            1263
0.1142060334E+04            1183
0.1148961000E+04            1124
0.1155861666E+04            1055
0.1162762333E+04             996
0.1169663000E+04             956
0.1176563666E+04             965
0.1183464334E+04             818
0.1190365000E+04             835
0.1197265666E+04             801
0.1204166333E+04             735
0.1211067000E+04             698
0.1217967666E+04             619
0.1224868334E+04             631
0.1231769000E+04             624
0.1238669666E+04             522
0.1245570333E+04             515
0.1252471000E+04             503
0.1259371666E+04             501
0.1266272334E+04             500
0.1273173000E+04             463
0.1280073666E+04             440
0.1286974333E+04             418
0.1293875000E+04             407
0.1300775667E+04             384
0.1307676334E+04             374
0.1314577000E+04             359
0.1321477666E+04             359
0.1328378334E+04             326
0.1335279000E+04             288
0.1342179667E+04             259
0.1349080334E+04             226
0.1355981000E+04             214
0.1362881666E+04             173
0.1369782334E+04             144
0.1376683000E+04             121
0.1383583667E+04             139
0.1390484334E+04             106
0.1397385000E+04             100
0.1404285666E+04              70
0.1411186334E+04              63
0.1418087000E+04              52
0.1424987667E+04              50
0.1431888334E+04              51
0.1438789000E+04              39
0.1445689666E+04              44
0.1452590334E+04              30
0.1459491000E+04              42
0.1466391667E+04              19
0.1473292334E+04              25
0.1480193000E+04              17
0.1487093666E+04              28
0.1493994334E+04              17
0.1500895000E+04              13
0.1507795667E+04              14
0.1514696334E+04               9
0.1521597000E+04               7
0.1528497666E+04               4
0.1535398334E+04               1
0.1542299000E+04               7
0.1549199667E+04               8
0.1556100334E+04               1
0.1563001000E+04               6
0.1569901666E+04               6
0.1576802334E+04               2
0.1583703000E+04               0
0.1590603667E+04               1
0.1597504334E+04               3
0.1604405000E+04               1
0.1611305666E+04               1
0.1618206334E+04               0
0.1625107000E+04               2
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0.1652709666E+04               1
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0.1666511000E+04               0
0.1673411667E+04               1
0.1680312334E+04               1
0.1687213000E+04               0
0.1694113666E+04               0
0.1701014334E+04               0
0.1707915000E+04               0
0.1714815667E+04               0
0.1721716334E+04               0
0.1728617000E+04               0
0.1735517666E+04               0
0.1742418334E+04               0
0.1749319000E+04               0
0.1756219667E+04               0
0.1763120334E+04               0
0.1770021000E+04               0
0.1776921666E+04               0
0.1783822334E+04               0
0.1790723000E+04               0
0.1797623667E+04               0
0.1804524334E+04               0
0.1811425000E+04               0
0.1818325666E+04               0
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0.1832127000E+04               0
0.1839027667E+04               0
0.1845928334E+04               0
0.1852829000E+04               0
0.1859729666E+04               0
0.1866630334E+04               0
0.1873531000E+04               0
0.1880431667E+04               0
0.1887332334E+04               0
0.1894233000E+04               0
0.1901133666E+04               0
0.1908034334E+04               0
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0.1921835667E+04               0
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0.1935637000E+04               0
0.1942537666E+04               0
0.1949438333E+04               0
0.1956339000E+04               0
0.1963239667E+04               0
0.1970140333E+04               0
0.1977041000E+04               0
0.1983941666E+04               0
0.1990842333E+04               0
0.1997743000E+04               0
0.2004643667E+04               0
0.2011544333E+04               0
0.2018445000E+04               0
0.2025345666E+04               0
0.2032246333E+04               0
0.2039147000E+04               0
0.2046047667E+04               0
0.2052948333E+04               0
0.2059849000E+04               0
0.2066749666E+04               0

1

# Discrete Fourier transformation from ASCII (for noob)

I am not familiar with Mathematica (I am a physicist programming in Fortran) and my knowledge of it is very limited, unfortunately.

I would like to perform the Fourier trasform of a lightcurve which I have as an ASCII table (time, photon counts).

I can import the table:

Data = Import["/path/light_1band.dat", "Table"]


and define the arrays of variables:

time = Table[Data[[i]][[1]], {i, 1, Dimensions[Data][[1]]}]
counts = Table[Data[[i]][[2]], {i, 1, Dimensions[Data][[1]]}]


which I can plot:

ListPlot[Data]


and it looks fine.

Now I would like to perform the Fourier transformation of this light curve and my guess is that I should use the discrete Fourier transformation (because I don't have an analytical expression for my light-curve). The final goal is to have two arrays consisting in the Real and Imaginary integrals as a function of a range of frequencies (v) chosen by me so that I can use them to calculate the phaselag as:

phaselag(v) = ATAN(-Imaginary(v),Real(v))

and then the timelag as:

timelag(v) = phaselag(v)/ 2*pie*v

I am kind of lost because it seems that mathematica can do so much more than what I need, however I don't how to get those integrals which would be already enough form me.

If I just do:

Fourier[Data]


I end up with a table of complex numbers which I don't know what they represents and if I plot it:

ListLinePlot[Abs[Fourier[Data]]]


the plot doesn't help me to understand what I get. I also tried to perform the integrals by myself because I am not sure that the command 'Fourier' can give me what I need but my pitiful tentative:

ftw[(w_)?NumberQ, t_, v_] :=  Total[v*Exp[I w t]]


is far from working (and I struggle a lot with mathematica language)

I am aware that most of my problems are related to my ignorance of how mathematica works (and also partially on how Fourier transformation works), but if you understood what I need to obtain, any suggestion will be appreciated !

Can you help me ?