How to find the exact value of the frequency by MATLAB?

I want to find the exact value of the frequency at which the peak is highest (represented by purple circle in the figure)on the left hand side of the figure. Is their a command or a way by which i can find that value? 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 ...     
    11324.9 11353 11330.8 11319.6 11313.2 11322.2 11294.4 11341 11345.3 11325.8 11359.3 11353.1 11330.7 11344.4 11361.9 11375.6 11338.2 11366.3 11349.5 11354.3 11373.5 11396.7 11387.6 11402 11415.8 11401.3 11416.9 11408.7 11371.5 11403.5 11437.4 11438.5 11452.5 11468.8 11428.4 11418.4 11395.3 11437.6 11409 11428.3 11375.6 11361.3 11343.6 11350.5 11357.6 11354.6 11394.5 11404.6 11449.5 11423 11451.8 11455.4 11472.9 11431.5 11453.7 11438.5 11433.6 11425.8 11413.5 11418.7 11395 11404.8 11367.5 11365.8 11351.3 11340.4 11374.3 11365 11397.8 11404 11387.6 11361.9 11354.5 11348.3 11297.2 11284.1 11308.6 11339.1 11354.3 11350.4 11350.6 11353.5 11353.7 11295.5 11303.3 11267.1 11333.3 11351.6 11330.9 11330.8 11336.9 11359.3 11361.6 11382.9 11339.5 11346 11403.5 11371.2 11381.8 11340.7...      
    11374.2 11360.8 11329.8 11361.6 11346.2 11343.8 11313.9 11294.8 11277.7 11289.3 11295 11302.2 11329.8 11339.1 11352.2 11348.7 11353.5 11354.6 11356.4 11336.3 11327 11366.5 11362.4 11372.7 11367 11353.1 11390.2 11391.7 11400.2 11387.9 11371.3 11377.6 11390 11442.7 11429 11445.1 11449.3 11452 11385.5 11395.6 11387.1 11355.4 11334.4 11346.1 11317.3 11337.9 11330.4 11339.2 11351.5 11336.3 11362.8 11342.8 11357.4 11355.3 11364.1 11333.1 11345.1 11355 11349.8 11376.7 11367.7 11394.9 11421.2 11434.2 11459.5 11448.3 11446.3 11432.8 11441.2 11380.6 11395.9 11394.5 11380.9 11364.8 11336.5 11346.2 11376.7 11392.8 11330.1 11361.6 11334.2 11341.4 11327.7 11315.8 11344.8 11328.6 11341.5 11350.6 11363.7 11383.3 11375 11398 11381.4 11411.2 11426.3 11440 11432.5 11438 11436.1 11467.1...      
    11506.6 11461.1 11493.6 11487.1 11461.8 11417.7 11429.3 11406.7 11400.5 11401 11387.3 11399.4 11395.1 11401.3 11379.5 11400.8 11408.7 11447.4 11460.4 11458.7 11432.9 11454.1 11480.8 11474.9 11504.1 11463.2 11530 11539 11531.9 11524.3 11484.2 11521.7 11490 11498.9 11451.1 11461.9 11486.6 11459.8 11463.9 11464.4 11513.1 11529 11534.2 11547.4 11564.6 11566.9 11485.5 11502.6 11471.7 11501.8 11466.6 11410.4 11426.5 11390.9 11426.5 11363.5 11366.3 11389.5 11368.3 11329.5 11315.5 11329.6 11310.7 11318.2 11272.7 11320.9 11320.9 11326.6 11351.1 11330.3 11391.4 11390.9 11388.4 11364.3 11354.7 11374.6 11355 11357.8 11332.7 11376.9 11348.4 11339.5 11382 11370 11343.6 11335.1 11321 11327.7 11294 11302.5 11302.6 11304.3 11299.9 11294.7 11298.9 11305.2 11341 11363.8 11384.5 11389.7...      
    11371.8 11390.4 11402.2 11387.3 11387.6 11387.3 11394.4 11447.1 11465 11431.5 11457.1 11460.6 11485.7 11491 11458.5 11440.9 11434.8 11454.9 11453.5 11463 11446.3 11475.9 11482.5 11457.3 11454.8 11445 11442.8 11440.9 11386.9 11412.6 11387.1 11402 11376.8 11425.7 11426 11426.7 11421.5 11438.4 11455.1 11423 11450 11429.3 11486 11504.3 11494.1 11510.8 11527.5 11562.5 11570.8 11520.7 11496.2 11508.6 11514.3 11457.7 11457.8 11435.8 11465 11475.5 11459.7 11462.8 11452.2 11499.4 11508 11478.9 11483.9 11479.6 11493.1 11451.4 11421.4 11366.3 11389.8 11385 11339.1 11322.4 11336.5 11346.9 11315.2 11328.6 11323 11348.3 11351.3 11346.5 11369.6 11400.5 11426.4 11432.4 11404.5 11415 11428.9 11446.8 11408.2 11417.9 11379.6 11379.4 11411 11383.2 11409.2 11443.8 11453.7 11455.9...      
    11420.4 11392.9 11395.4 11389.9 11358.4 11370.3 11404.4 11406 11418.9 11404.7 11460.1 11472.4 11510.2 11472 11457.3 11493.7 11507.3 11512.8 11489.1 11481.3 11481.6 11451.9 11423.8 11336.1 11413.5 11412.1 11376.1 11368.6 11371.8 11361.7 11320.5 11294.2 11268.4 11302.5 11344.5 11320.8 11345.4 11308.4 11327.4 11337.9 11340 11354.1 11355.1 11376.6 11406.4 11422.9 11434.4 11441.6 11457.7 11474.1 11487.9 11489.5 11461.2 11477.4 11464.9 11506.4 11484.7 11476.8 11466.2 11746 11060.5 11805 11714 11676.6 11674.9 11609.2 11516.9 11505 11534.9 11527.1 11514.4 11513.6 11535.7 11450 11435.1 11390.1 11426.6 11406 11385.3 11359.2 11332.5 11327.7 11302.2 11296.2 11267 11269.5 11246.4 11260.3 11284.6 11268.1 11257.5 11258.9 11252.8 11259.1 11304.2 11286.2 11319.8 11441.8 11558.1 11648.4...      
    11671.6 11658.8 11612.9 11656.8 11823 11659.9 11559.5 11550 11601.1 11528.9 11489.8 11456.9 11447 11441.3 11456.1 11463.4 11443.9 11408.3 11414.5 11406.2 11408.4 11438.5 11427.3 11461.3 11444.7 11421.3 11413.1 11407.6 11421.8 11395 11379.2 11344.8 11333.3 11299 11296.6 11275.3 11275.4 11275.3 11268.8 11279.5 11304.4 11335.2 11284.6 11261.9 11256.3 11237.6 11242.8 11250.3 11298.5 11313.5 11262.5 11254.6 11256.5 11259.6 11258.3 11257.5 11269.6 11321.6 11369.7 11379.5 11356.1 11311.4 11309.1 11296.4 11322.4 11369.7 11398.9 11419.5 11399.9 11398.2 11425.6 11452.6 11476 11492 11438 11413.4 11441.6 11498.6 11481.6 11469.9 11448.4 11434.1 11452.9 11483.7 11463 11470.8 11447.8 11445.5 11446.8 11424.1 11438.2 11465.9 11454.2 11446.3 11448.6 11431.1 11428.8 11416.1 11407.1 11412.1...      
    11448.8 11449.7 11442.1 11424.9 11409.3 11402.4 11386.8 11413.2 11434.9 11447.9 11441.4 11434.9 11405.2 11414.3 11416.5 11437.9 11455.2 11404.8 11422.6 11435.6 11424.7 11457.5 11439 11442.2 11398.3 11381 11424.2 11421.2 11391 11390.9 11384.8 11402 11396.7 11382.7 11388.9 11357.5 11377.2 11353.7 11334.6 11346.5 11335.4 11330.6 11321 11329.2 11354.6 11369.8 11361 11363 11355.9 11399.1 11394 11410.7 11394 11405.1 11407.4 11399.2 11438 11435.8 11429.7 11419.8 11387.2 11375.3 11381.1 11381.3 11397.8 11383.4 11364.6 11332.7 11317 11345.3 11322 11359.8 11337.2 11331.4 11319.2 11321.3 11325 11334.7 11360.3 11356 11337.7 11343.6 11353.7 11379.3 11436.6 11428.2 11437.8 11411.4 11438.8 11461.5 11468.5 11489.3 11459.3 11437.7 11415.6 11398.6 11418.8 11415.6 11394.3 11380 ...       
    11365.9 11366.6 11369.4 11386.2 11405.7 11349 11372.3 11370.5 11370.2 11402.6 11385 11401.8 11382.5 11362.5 11353.6 11368.9 11365.3 11377.3 11375.3 11385.2 11364.7 11357 11366.8 11337.1 11348.1 11316.3 11308.3 11322.2 11311 11341.8 11350.1 11340.1 11348.3 11338.4 11379.9 11395.1 11368.1 11363.4 11342.3 11329.5 11317.9 11318.7 11304.5 11256.4 11277.6 11247.3 11264.2 11247.9 11245.6 11243.5 11257.1 11289.5 11250.5 11252.9 11243.2 11278.9 11323.5 11299.4 11328.1 11306.9 11311.5 11317.8 11308.3 11302.3 11276.2 11295.2 11252.7 11267.4 11268.3 11265.8 11271.8 11266.6 11280.2 11273.3 11300.6 11280.5 11298.7 11341.9 11336.2 11354.5 11351 11344.7 11346.5 11321.8 11358.6 11340.5 11352.6 11333.3 11347.1 11369.5 11352.9 11359.9 11335.2 11308.9 11331.4 11319.5 11344.5 11337.1 11352.8 11371.9 ...      
    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))

Answer 1

[Walter Roberson]

No, there is no command in MATLAB that can tell you the exact frequency of a peak. The most you would be able to tell is the frequency bin involved and the relative width of the bin.

It is never possible to tell frequency without having some information that relates the data to time. That could be sample interval (such as 1 hour between samples), or sample frequency (such as 20 Hz), or total duration. fft just gets passed a list of sample values assumed to be uniformly sampled in time, and cannot tell whether the data was sampled nanoseconds apart or hours apart or millennia apart.

If you did have time information then it would be possible to calculate frequency, but only approximately. For example if the samples were taken at 100 Hz for 1/4 second then you would not be able to distinguish between 22.4 Hz and 22.8 Hz -- and you cannot be sure that both of them will land on the same bin: one might round into the next bin, especially if there is a notable imaginary (phase) component.

Answer 2

[Chunru]

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 ...     
    11324.9 11353 11330.8 11319.6 11313.2 11322.2 11294.4 11341 11345.3 11325.8 11359.3 11353.1 11330.7 11344.4 11361.9 11375.6 11338.2 11366.3 11349.5 11354.3 11373.5 11396.7 11387.6 11402 11415.8 11401.3 11416.9 11408.7 11371.5 11403.5 11437.4 11438.5 11452.5 11468.8 11428.4 11418.4 11395.3 11437.6 11409 11428.3 11375.6 11361.3 11343.6 11350.5 11357.6 11354.6 11394.5 11404.6 11449.5 11423 11451.8 11455.4 11472.9 11431.5 11453.7 11438.5 11433.6 11425.8 11413.5 11418.7 11395 11404.8 11367.5 11365.8 11351.3 11340.4 11374.3 11365 11397.8 11404 11387.6 11361.9 11354.5 11348.3 11297.2 11284.1 11308.6 11339.1 11354.3 11350.4 11350.6 11353.5 11353.7 11295.5 11303.3 11267.1 11333.3 11351.6 11330.9 11330.8 11336.9 11359.3 11361.6 11382.9 11339.5 11346 11403.5 11371.2 11381.8 11340.7...      
    11374.2 11360.8 11329.8 11361.6 11346.2 11343.8 11313.9 11294.8 11277.7 11289.3 11295 11302.2 11329.8 11339.1 11352.2 11348.7 11353.5 11354.6 11356.4 11336.3 11327 11366.5 11362.4 11372.7 11367 11353.1 11390.2 11391.7 11400.2 11387.9 11371.3 11377.6 11390 11442.7 11429 11445.1 11449.3 11452 11385.5 11395.6 11387.1 11355.4 11334.4 11346.1 11317.3 11337.9 11330.4 11339.2 11351.5 11336.3 11362.8 11342.8 11357.4 11355.3 11364.1 11333.1 11345.1 11355 11349.8 11376.7 11367.7 11394.9 11421.2 11434.2 11459.5 11448.3 11446.3 11432.8 11441.2 11380.6 11395.9 11394.5 11380.9 11364.8 11336.5 11346.2 11376.7 11392.8 11330.1 11361.6 11334.2 11341.4 11327.7 11315.8 11344.8 11328.6 11341.5 11350.6 11363.7 11383.3 11375 11398 11381.4 11411.2 11426.3 11440 11432.5 11438 11436.1 11467.1...      
    11506.6 11461.1 11493.6 11487.1 11461.8 11417.7 11429.3 11406.7 11400.5 11401 11387.3 11399.4 11395.1 11401.3 11379.5 11400.8 11408.7 11447.4 11460.4 11458.7 11432.9 11454.1 11480.8 11474.9 11504.1 11463.2 11530 11539 11531.9 11524.3 11484.2 11521.7 11490 11498.9 11451.1 11461.9 11486.6 11459.8 11463.9 11464.4 11513.1 11529 11534.2 11547.4 11564.6 11566.9 11485.5 11502.6 11471.7 11501.8 11466.6 11410.4 11426.5 11390.9 11426.5 11363.5 11366.3 11389.5 11368.3 11329.5 11315.5 11329.6 11310.7 11318.2 11272.7 11320.9 11320.9 11326.6 11351.1 11330.3 11391.4 11390.9 11388.4 11364.3 11354.7 11374.6 11355 11357.8 11332.7 11376.9 11348.4 11339.5 11382 11370 11343.6 11335.1 11321 11327.7 11294 11302.5 11302.6 11304.3 11299.9 11294.7 11298.9 11305.2 11341 11363.8 11384.5 11389.7...      
    11371.8 11390.4 11402.2 11387.3 11387.6 11387.3 11394.4 11447.1 11465 11431.5 11457.1 11460.6 11485.7 11491 11458.5 11440.9 11434.8 11454.9 11453.5 11463 11446.3 11475.9 11482.5 11457.3 11454.8 11445 11442.8 11440.9 11386.9 11412.6 11387.1 11402 11376.8 11425.7 11426 11426.7 11421.5 11438.4 11455.1 11423 11450 11429.3 11486 11504.3 11494.1 11510.8 11527.5 11562.5 11570.8 11520.7 11496.2 11508.6 11514.3 11457.7 11457.8 11435.8 11465 11475.5 11459.7 11462.8 11452.2 11499.4 11508 11478.9 11483.9 11479.6 11493.1 11451.4 11421.4 11366.3 11389.8 11385 11339.1 11322.4 11336.5 11346.9 11315.2 11328.6 11323 11348.3 11351.3 11346.5 11369.6 11400.5 11426.4 11432.4 11404.5 11415 11428.9 11446.8 11408.2 11417.9 11379.6 11379.4 11411 11383.2 11409.2 11443.8 11453.7 11455.9...      
    11420.4 11392.9 11395.4 11389.9 11358.4 11370.3 11404.4 11406 11418.9 11404.7 11460.1 11472.4 11510.2 11472 11457.3 11493.7 11507.3 11512.8 11489.1 11481.3 11481.6 11451.9 11423.8 11336.1 11413.5 11412.1 11376.1 11368.6 11371.8 11361.7 11320.5 11294.2 11268.4 11302.5 11344.5 11320.8 11345.4 11308.4 11327.4 11337.9 11340 11354.1 11355.1 11376.6 11406.4 11422.9 11434.4 11441.6 11457.7 11474.1 11487.9 11489.5 11461.2 11477.4 11464.9 11506.4 11484.7 11476.8 11466.2 11746 11060.5 11805 11714 11676.6 11674.9 11609.2 11516.9 11505 11534.9 11527.1 11514.4 11513.6 11535.7 11450 11435.1 11390.1 11426.6 11406 11385.3 11359.2 11332.5 11327.7 11302.2 11296.2 11267 11269.5 11246.4 11260.3 11284.6 11268.1 11257.5 11258.9 11252.8 11259.1 11304.2 11286.2 11319.8 11441.8 11558.1 11648.4...      
    11671.6 11658.8 11612.9 11656.8 11823 11659.9 11559.5 11550 11601.1 11528.9 11489.8 11456.9 11447 11441.3 11456.1 11463.4 11443.9 11408.3 11414.5 11406.2 11408.4 11438.5 11427.3 11461.3 11444.7 11421.3 11413.1 11407.6 11421.8 11395 11379.2 11344.8 11333.3 11299 11296.6 11275.3 11275.4 11275.3 11268.8 11279.5 11304.4 11335.2 11284.6 11261.9 11256.3 11237.6 11242.8 11250.3 11298.5 11313.5 11262.5 11254.6 11256.5 11259.6 11258.3 11257.5 11269.6 11321.6 11369.7 11379.5 11356.1 11311.4 11309.1 11296.4 11322.4 11369.7 11398.9 11419.5 11399.9 11398.2 11425.6 11452.6 11476 11492 11438 11413.4 11441.6 11498.6 11481.6 11469.9 11448.4 11434.1 11452.9 11483.7 11463 11470.8 11447.8 11445.5 11446.8 11424.1 11438.2 11465.9 11454.2 11446.3 11448.6 11431.1 11428.8 11416.1 11407.1 11412.1...      
    11448.8 11449.7 11442.1 11424.9 11409.3 11402.4 11386.8 11413.2 11434.9 11447.9 11441.4 11434.9 11405.2 11414.3 11416.5 11437.9 11455.2 11404.8 11422.6 11435.6 11424.7 11457.5 11439 11442.2 11398.3 11381 11424.2 11421.2 11391 11390.9 11384.8 11402 11396.7 11382.7 11388.9 11357.5 11377.2 11353.7 11334.6 11346.5 11335.4 11330.6 11321 11329.2 11354.6 11369.8 11361 11363 11355.9 11399.1 11394 11410.7 11394 11405.1 11407.4 11399.2 11438 11435.8 11429.7 11419.8 11387.2 11375.3 11381.1 11381.3 11397.8 11383.4 11364.6 11332.7 11317 11345.3 11322 11359.8 11337.2 11331.4 11319.2 11321.3 11325 11334.7 11360.3 11356 11337.7 11343.6 11353.7 11379.3 11436.6 11428.2 11437.8 11411.4 11438.8 11461.5 11468.5 11489.3 11459.3 11437.7 11415.6 11398.6 11418.8 11415.6 11394.3 11380 ...       
    11365.9 11366.6 11369.4 11386.2 11405.7 11349 11372.3 11370.5 11370.2 11402.6 11385 11401.8 11382.5 11362.5 11353.6 11368.9 11365.3 11377.3 11375.3 11385.2 11364.7 11357 11366.8 11337.1 11348.1 11316.3 11308.3 11322.2 11311 11341.8 11350.1 11340.1 11348.3 11338.4 11379.9 11395.1 11368.1 11363.4 11342.3 11329.5 11317.9 11318.7 11304.5 11256.4 11277.6 11247.3 11264.2 11247.9 11245.6 11243.5 11257.1 11289.5 11250.5 11252.9 11243.2 11278.9 11323.5 11299.4 11328.1 11306.9 11311.5 11317.8 11308.3 11302.3 11276.2 11295.2 11252.7 11267.4 11268.3 11265.8 11271.8 11266.6 11280.2 11273.3 11300.6 11280.5 11298.7 11341.9 11336.2 11354.5 11351 11344.7 11346.5 11321.8 11358.6 11340.5 11352.6 11333.3 11347.1 11369.5 11352.9 11359.9 11335.2 11308.9 11331.4 11319.5 11344.5 11337.1 11352.8 11371.9 ...      
    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));
% specify a region to search for max
r = [10 600]; 
[Fmax, idx] = max(real(Fx([r(1):r(2)])));       % findpeaks are more sophiscated
idx = idx + (10-1);
hold on
plot(idx, real(Fx(idx)), 'ro')

idx, real(Fx(idx))

idx = 33

ans = 1.0703e+04

[Walter Roberson]

It might be better to use abs() instead of real(). The out-of-phase parts can have a lot of power.

[Walter Roberson]

Should be adding r(1) to idx, not 10.

[Chunru]

To be general, adding r(1)-1.

[Walter Roberson]

You already have the -1 in the code ;-)

idx = idx + r(1) - 1;

[Haya Ali]

what is idx here?

[Haya Ali]

Can you please elaborate what each of the step is doing?

r = [10 600]; 
[Fmax, idx] = max(real(Fx([r(1):r(2)])));       % findpeaks are more sophiscated
idx = idx + (10-1);
hold on
plot(idx, real(Fx(idx)), 'ro')

Answer 3

[Simon Chan]

May use threshold, which find another peaks on the left hand side

plot(real(Fx));
hold on
threshold = 1e4;
pos = find(real(Fx)>threshold);
plot(pos, real(Fx(pos)), 'go');

pos =

           3          33        1169        1199
           
  real(Fx(pos))

ans =

   1.0e+04 *

    1.1762    1.0703    1.0703    1.1762

[Image Analyst]

Just to state the obvious (but in case someone doesn't realize) - peaks on the left and right represent the same frequency, just negative of each other, like 10 Hz and -10 Hz.

[Haya Ali]

How did you set the threshold value?

[Simon Chan]

In my example, it is obviously selected by observation based on the values in the figure.

In the real case, It really depends on what you need. If you want the maximum point in the entire spectrum, you may use the following.

Of course, you got two values in the answer (one on the left and one on the right)

threshold = max(real(Fx));
pos = find(real(Fx)==threshold)

[Haya Ali]

Thanks a lot!

[Haya Ali]

What is this command calculating?

pos = find(real(Fx)==threshold)

[Simon Chan]

Better to look at the following link about the command 'find'.

Find indices and values of nonzero elements

In this case, it is finding the indices where the value of real(Fx) equals to the threshold value.

[Haya Ali]

Please see the plot is not showing anything in the case of abs of x.

close all; clear all; clc;
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 ...     
    11324.9 11353 11330.8 11319.6 11313.2 11322.2 11294.4 11341 11345.3 11325.8 11359.3 11353.1 11330.7 11344.4 11361.9 11375.6 11338.2 11366.3 11349.5 11354.3 11373.5 11396.7 11387.6 11402 11415.8 11401.3 11416.9 11408.7 11371.5 11403.5 11437.4 11438.5 11452.5 11468.8 11428.4 11418.4 11395.3 11437.6 11409 11428.3 11375.6 11361.3 11343.6 11350.5 11357.6 11354.6 11394.5 11404.6 11449.5 11423 11451.8 11455.4 11472.9 11431.5 11453.7 11438.5 11433.6 11425.8 11413.5 11418.7 11395 11404.8 11367.5 11365.8 11351.3 11340.4 11374.3 11365 11397.8 11404 11387.6 11361.9 11354.5 11348.3 11297.2 11284.1 11308.6 11339.1 11354.3 11350.4 11350.6 11353.5 11353.7 11295.5 11303.3 11267.1 11333.3 11351.6 11330.9 11330.8 11336.9 11359.3 11361.6 11382.9 11339.5 11346 11403.5 11371.2 11381.8 11340.7...      
    11374.2 11360.8 11329.8 11361.6 11346.2 11343.8 11313.9 11294.8 11277.7 11289.3 11295 11302.2 11329.8 11339.1 11352.2 11348.7 11353.5 11354.6 11356.4 11336.3 11327 11366.5 11362.4 11372.7 11367 11353.1 11390.2 11391.7 11400.2 11387.9 11371.3 11377.6 11390 11442.7 11429 11445.1 11449.3 11452 11385.5 11395.6 11387.1 11355.4 11334.4 11346.1 11317.3 11337.9 11330.4 11339.2 11351.5 11336.3 11362.8 11342.8 11357.4 11355.3 11364.1 11333.1 11345.1 11355 11349.8 11376.7 11367.7 11394.9 11421.2 11434.2 11459.5 11448.3 11446.3 11432.8 11441.2 11380.6 11395.9 11394.5 11380.9 11364.8 11336.5 11346.2 11376.7 11392.8 11330.1 11361.6 11334.2 11341.4 11327.7 11315.8 11344.8 11328.6 11341.5 11350.6 11363.7 11383.3 11375 11398 11381.4 11411.2 11426.3 11440 11432.5 11438 11436.1 11467.1...      
    11506.6 11461.1 11493.6 11487.1 11461.8 11417.7 11429.3 11406.7 11400.5 11401 11387.3 11399.4 11395.1 11401.3 11379.5 11400.8 11408.7 11447.4 11460.4 11458.7 11432.9 11454.1 11480.8 11474.9 11504.1 11463.2 11530 11539 11531.9 11524.3 11484.2 11521.7 11490 11498.9 11451.1 11461.9 11486.6 11459.8 11463.9 11464.4 11513.1 11529 11534.2 11547.4 11564.6 11566.9 11485.5 11502.6 11471.7 11501.8 11466.6 11410.4 11426.5 11390.9 11426.5 11363.5 11366.3 11389.5 11368.3 11329.5 11315.5 11329.6 11310.7 11318.2 11272.7 11320.9 11320.9 11326.6 11351.1 11330.3 11391.4 11390.9 11388.4 11364.3 11354.7 11374.6 11355 11357.8 11332.7 11376.9 11348.4 11339.5 11382 11370 11343.6 11335.1 11321 11327.7 11294 11302.5 11302.6 11304.3 11299.9 11294.7 11298.9 11305.2 11341 11363.8 11384.5 11389.7...      
    11371.8 11390.4 11402.2 11387.3 11387.6 11387.3 11394.4 11447.1 11465 11431.5 11457.1 11460.6 11485.7 11491 11458.5 11440.9 11434.8 11454.9 11453.5 11463 11446.3 11475.9 11482.5 11457.3 11454.8 11445 11442.8 11440.9 11386.9 11412.6 11387.1 11402 11376.8 11425.7 11426 11426.7 11421.5 11438.4 11455.1 11423 11450 11429.3 11486 11504.3 11494.1 11510.8 11527.5 11562.5 11570.8 11520.7 11496.2 11508.6 11514.3 11457.7 11457.8 11435.8 11465 11475.5 11459.7 11462.8 11452.2 11499.4 11508 11478.9 11483.9 11479.6 11493.1 11451.4 11421.4 11366.3 11389.8 11385 11339.1 11322.4 11336.5 11346.9 11315.2 11328.6 11323 11348.3 11351.3 11346.5 11369.6 11400.5 11426.4 11432.4 11404.5 11415 11428.9 11446.8 11408.2 11417.9 11379.6 11379.4 11411 11383.2 11409.2 11443.8 11453.7 11455.9...      
    11420.4 11392.9 11395.4 11389.9 11358.4 11370.3 11404.4 11406 11418.9 11404.7 11460.1 11472.4 11510.2 11472 11457.3 11493.7 11507.3 11512.8 11489.1 11481.3 11481.6 11451.9 11423.8 11336.1 11413.5 11412.1 11376.1 11368.6 11371.8 11361.7 11320.5 11294.2 11268.4 11302.5 11344.5 11320.8 11345.4 11308.4 11327.4 11337.9 11340 11354.1 11355.1 11376.6 11406.4 11422.9 11434.4 11441.6 11457.7 11474.1 11487.9 11489.5 11461.2 11477.4 11464.9 11506.4 11484.7 11476.8 11466.2 11746 11060.5 11805 11714 11676.6 11674.9 11609.2 11516.9 11505 11534.9 11527.1 11514.4 11513.6 11535.7 11450 11435.1 11390.1 11426.6 11406 11385.3 11359.2 11332.5 11327.7 11302.2 11296.2 11267 11269.5 11246.4 11260.3 11284.6 11268.1 11257.5 11258.9 11252.8 11259.1 11304.2 11286.2 11319.8 11441.8 11558.1 11648.4...      
    11671.6 11658.8 11612.9 11656.8 11823 11659.9 11559.5 11550 11601.1 11528.9 11489.8 11456.9 11447 11441.3 11456.1 11463.4 11443.9 11408.3 11414.5 11406.2 11408.4 11438.5 11427.3 11461.3 11444.7 11421.3 11413.1 11407.6 11421.8 11395 11379.2 11344.8 11333.3 11299 11296.6 11275.3 11275.4 11275.3 11268.8 11279.5 11304.4 11335.2 11284.6 11261.9 11256.3 11237.6 11242.8 11250.3 11298.5 11313.5 11262.5 11254.6 11256.5 11259.6 11258.3 11257.5 11269.6 11321.6 11369.7 11379.5 11356.1 11311.4 11309.1 11296.4 11322.4 11369.7 11398.9 11419.5 11399.9 11398.2 11425.6 11452.6 11476 11492 11438 11413.4 11441.6 11498.6 11481.6 11469.9 11448.4 11434.1 11452.9 11483.7 11463 11470.8 11447.8 11445.5 11446.8 11424.1 11438.2 11465.9 11454.2 11446.3 11448.6 11431.1 11428.8 11416.1 11407.1 11412.1...      
    11448.8 11449.7 11442.1 11424.9 11409.3 11402.4 11386.8 11413.2 11434.9 11447.9 11441.4 11434.9 11405.2 11414.3 11416.5 11437.9 11455.2 11404.8 11422.6 11435.6 11424.7 11457.5 11439 11442.2 11398.3 11381 11424.2 11421.2 11391 11390.9 11384.8 11402 11396.7 11382.7 11388.9 11357.5 11377.2 11353.7 11334.6 11346.5 11335.4 11330.6 11321 11329.2 11354.6 11369.8 11361 11363 11355.9 11399.1 11394 11410.7 11394 11405.1 11407.4 11399.2 11438 11435.8 11429.7 11419.8 11387.2 11375.3 11381.1 11381.3 11397.8 11383.4 11364.6 11332.7 11317 11345.3 11322 11359.8 11337.2 11331.4 11319.2 11321.3 11325 11334.7 11360.3 11356 11337.7 11343.6 11353.7 11379.3 11436.6 11428.2 11437.8 11411.4 11438.8 11461.5 11468.5 11489.3 11459.3 11437.7 11415.6 11398.6 11418.8 11415.6 11394.3 11380 ...       
    11365.9 11366.6 11369.4 11386.2 11405.7 11349 11372.3 11370.5 11370.2 11402.6 11385 11401.8 11382.5 11362.5 11353.6 11368.9 11365.3 11377.3 11375.3 11385.2 11364.7 11357 11366.8 11337.1 11348.1 11316.3 11308.3 11322.2 11311 11341.8 11350.1 11340.1 11348.3 11338.4 11379.9 11395.1 11368.1 11363.4 11342.3 11329.5 11317.9 11318.7 11304.5 11256.4 11277.6 11247.3 11264.2 11247.9 11245.6 11243.5 11257.1 11289.5 11250.5 11252.9 11243.2 11278.9 11323.5 11299.4 11328.1 11306.9 11311.5 11317.8 11308.3 11302.3 11276.2 11295.2 11252.7 11267.4 11268.3 11265.8 11271.8 11266.6 11280.2 11273.3 11300.6 11280.5 11298.7 11341.9 11336.2 11354.5 11351 11344.7 11346.5 11321.8 11358.6 11340.5 11352.6 11333.3 11347.1 11369.5 11352.9 11359.9 11335.2 11308.9 11331.4 11319.5 11344.5 11337.1 11352.8 11371.9 ...      
    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));
    threshold = max(abs(Fx))
    pos = find(abs(Fx)==threshold)
    plot(pos, abs(Fx(pos)), 'go');

[Simon Chan]

Need to plot the spectrum first:

plot(abs(Fx));
hold on
threshold = max(abs(Fx));
pos = find(abs(Fx)==threshold);
plot(pos, abs(Fx(pos)), 'go');

[Haya Ali]

Much Obliged!