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From a patient we received a periodic wave representing the blood flow (measured in kg/h) over time.

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Problem description:

From a patient we received a periodic wave representing the blood flow (measured in kg/h) over time. The data containing respectively the time in seconds and the corresponding blood flow values in kg/h per time point is found below:

0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
2,2
2,4
2,6
2,8
3
3,2
3,4
3,6
3,8
4
4,2
4,4
4,6
4,8
5
46,120
47,154
51,547
59,017
68,093
76,425
83,073
86,914
88,064
87,224
84,216
79,436
73,656
67,657
63,181
60,510
59,256
58,172
56,726
54,540
52,112
50,374
49,356
48,457
47,399
46,523

The plot of this data looks as follows:

The problem is the next:

We need a fourier transform performed on the wave shown in the graph. So that signal has to be decomposed into a superposition of sine waves. This way we can really closely mimic the data and it makes it more repeatable. So I need the function containing the superposition of sine waves with each its own amplitude and fase shift. I need a clear scientific answer containing all the in between steps so we can use it in the research. I need it up till the 4th order if that is possible.

So when I receive the superposition and let it run over time it gives me the exact representation of the file provided above. If anything is not clear let me know.

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