# 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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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.

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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11359.4 11373.2 11339.4 11340.5 11343.4 11326.3 11332 11300.9 11335.2 11319.5 11327 11353.4 11358.1 11376.5 11356.3 11369.2 11381.7 11364.1 11392.4 11363.8 11376.8 11371.5 11366 11401 11366 11374.2 11347.6 11350.8 11354.1 11348.3 11377.9 11350.9 11384.9 11370.2 11378.9 11410.1 11399.8 11422.8 11390.8 11410.8 11377.9 11365.6 11390 11363 11373.6 11358.8 11350.5 11370.1 11377.4 11421.5 11392.7 11429.5 11429.2 11440.5 11469.2 11415.8 11402.9 11349.8 11338.3 11312.8 11319.9 11323.2 11316.9 11320.3 11304.7 11311 11360.6 11354.3 11396.2 11376.8 11390.6 11404.5 11413.7 11394.7 11377.3 11346.3 11358.1 11339.4 11379.6 11358.9 11372.3 11377.1 11367.6 11389.9 11360 11408.8 11376 11373.3 11344.2 11342.9 11355.1 11328.9 11348.1 11348.7 11350.8 11371.7 11362.2 11360.3 11338.7 11319.6 ...
11306.7 11320.4 11350.3 11314.6 11356.8 11356.7 11398.8 11377.8 11368 11365.7 11357.6 11368.1 11362.3 11385.3 11380.3 11398.1 11368.4 11390.9 11410.7 11371.2 11386.2 11375.6 11370.2 11401.5 11394.5 11388.7 11370.1 11391.7 11399.6 11393.8 11398.6 11417.7 11413.5 11397 11432.9 11415.3 11423.2 11402.4 11399.1 11402.7 11390.5 11421.6 11378.3 11409.1 11408.5 11408.3 11442.2 11410.2 11449.1 11428.1 11444.5 11461.2 11437.1 11380 11384.3 11380.8 11356.6 11371.3 11360.7 11384.6 11389.7 11364.9 11370.7 11354 11356.8 11380.4 11371.1 11396.3 11370 11392.6 11369.9 11382.5 11372.3 11359.6 11335 11324.7 11337.8 11338.7 11345 11321.7 11350.4 11345.6 11366.6 11346 11325 11331.1 11336.8 11337.5 11323.5 11337.6 11310.2 11316.2 11367.4 11346.4 11372 11379.5 11389.3 11374.4 11372.5 11371.7 ...
11356 11354.2 11335.5 11372.6 11370.7 11386.8 11363.4 11358.3 11397.9 11383.7 11396.8 11397.8 11385.2 11401.2 11395.9 11398.1 11394 11399.5 11373.6 11388.2 11377.5 11394.6 11414 11393.3 11406.4 11405.6 11410.5 11434.6 11413.3 11453.9 11439.2 11457.6 11458.4 11446.7 11439.1 11433.6 11441.8 11414.7 11436.4 11403.5 11450.9 11432.5 11439.6 11473.3 11449.6 11463.1 11452.3 11427.2 11401.4 11405.6 11360.7 11366.5 11336.1 11317.6 11289.2 11306.6 11306.7 11302.1 11350.6 11343.2 11368.7 11370 11365.4 11334.1 11317.6 11336 11305.5 11330.4 11306.5 11317.9 11321.9 11313.5 11344.5 11307.2 11335.5 11316.7 11334.7 11313.4 11326.3 11313.2 11307.2 11334.8 11321 11323.6 11317.9 11338.3 11330.7 11314.4 11334.7 11335.3 11353.3 11341.7 11366.5 11351.7 11353.6 11364.3 11361 11351.9 11337.9 11372.8];
Fx = fft(x - mean(x));
plot(real(Fx))
plot(imag(Fx))
plot(real(Fx(1:100)))
It isn't clear what "optimal frequency" means
Haya Ali on 11 Jul 2021
Thanks a lot!