# How to apply fourier analysis on the data given?

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Haya Ali on 10 Jul 2021
Commented: Haya Ali on 11 Jul 2021
I have to apply the fourier analysis on the vector x given below. How to apply the fourier transform and find the optimal frequency? Please help
x=[11500.2 11477.9 11417.3 11426.4 11413 11382.9 11375.1 11347.9 11351.1 11329.3 11318.9 11343.4 11360.7 11378.4 11414.2 11408.2 11413.6 11449.4 11444.1 11421.4 11388.5 11429.3 11438.1 11432.9 11408.2 11434.3 11444.8 11443.5 11491.8 11503.8 11581.8 11525.9 11529.5 11557.6 11523 11516 11504.1 11492.9 11480.3 11495.9 11445.1 11437.7 11468.5 11463 11488.5 11470.3 11491.1 11480.2 11488.9 11453.8 11456 11434.5 11460.6 11456.1 11454 11468.3 11464.4 11501 11453.8 11474.2 11458.2 11452.8 11434.6 11447.3 11379.5 11396.4 11409.9 11405.6 11433.3 11435.6 11434.2 11415.5 11483.6 11434.6 11452.2 11471.5 11445 11462.6 11433.3 11440.2 11442.3 11456 11408.6 11399.7 11369.8 11372.6 11401.4 11405 11426.6 11430.3 11405.6 11409.8 11405 11399.7 11381.2 11392.5 11383.6 11365.8 11362.4 11347.8 ...
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##### 1 CommentShow -1 older commentsHide -1 older comments
KSSV on 10 Jul 2021
It is striaght forward. Read it here: https://in.mathworks.com/help/matlab/ref/fft.html you got examples too right? Go through one example.

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### Accepted Answer

Walter Roberson on 10 Jul 2021
x=[11500.2 11477.9 11417.3 11426.4 11413 11382.9 11375.1 11347.9 11351.1 11329.3 11318.9 11343.4 11360.7 11378.4 11414.2 11408.2 11413.6 11449.4 11444.1 11421.4 11388.5 11429.3 11438.1 11432.9 11408.2 11434.3 11444.8 11443.5 11491.8 11503.8 11581.8 11525.9 11529.5 11557.6 11523 11516 11504.1 11492.9 11480.3 11495.9 11445.1 11437.7 11468.5 11463 11488.5 11470.3 11491.1 11480.2 11488.9 11453.8 11456 11434.5 11460.6 11456.1 11454 11468.3 11464.4 11501 11453.8 11474.2 11458.2 11452.8 11434.6 11447.3 11379.5 11396.4 11409.9 11405.6 11433.3 11435.6 11434.2 11415.5 11483.6 11434.6 11452.2 11471.5 11445 11462.6 11433.3 11440.2 11442.3 11456 11408.6 11399.7 11369.8 11372.6 11401.4 11405 11426.6 11430.3 11405.6 11409.8 11405 11399.7 11381.2 11392.5 11383.6 11365.8 11362.4 11347.8 ...
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Fx = fft(x - mean(x));
plot(real(Fx))
plot(imag(Fx))
plot(real(Fx(1:100)))
It isn't clear what "optimal frequency" means
##### 3 CommentsShow 1 older commentHide 1 older comment
Walter Roberson on 10 Jul 2021
When you fft(), the first element of the output works out to be sum() of the input signal. Your data is all over 11000 so that would be roughly 11200*length() of the signal. That would be a huge spike in the first entry that would distort the graph completely.
Mathematically, sum() of a signal equals mean() of the signal times length of the signal, since mean is defined as sum divided by length. So if you take x-mean(x) and sum that then the result will be 0 in the first entry. But it will not affect the shape of the rest of the fft.
I indexed to 100 to zoom in on the plot. We can see from the complete plot that the spikes are largest closer to the beginning, so if you want to find frequency then you would probably zoom in on abs(x). It is not incorrect to think of the indexing as being about controlling the frequency range.
However remember that the fft above is in radians per unit time, not in absolute frequency. You would need to know the sampling frequency or sampling interval or totalssignal time in order to determine the absolute frequency.
Haya Ali on 11 Jul 2021
Thanks a lot!

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