# My snipet code have 3 harmonics, second's amplitude is maximum, but abs(fft(X)) returns first as maximum. I use MATLAB R2022a.

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Georges Theodosiou on 14 Sep 2022
In Xn first harmonic's amplitude is 170, second's 220, and third's 150. But abs(fft(Xn) returns maximum first's. Thanks in advance. It is executing in R2022a version.
SampFreq = 16000;
Segm = 1:2048;
Pitch = 45;
FirstHarmAngles = Pitch*2*pi/SampFreq*Segm+1.9*pi;
SinFirstHarmAngles = sin(FirstHarmAngles);
SecondHarmAngles = Pitch*2*2*pi/SampFreq*Segm+2.9*pi;
SinSecondHarmAngles = sin(SecondHarmAngles);
ThirdHarmAngles = Pitch*3*2*pi/SampFreq*Segm+0.3*pi;
SinThirdHarmAngles = sin(ThirdHarmAngles);
Xn = 170*SinFirstHarmAngles+220*SinSecondHarmAngles+150*...
SinThirdHarmAngles;
ABS = abs(fft(Xn))
ABS = 1×2048
1.0e+05 * 0.0359 0.0414 0.0581 0.0907 0.1634 0.4385 1.6552 0.4040 0.3079 0.3324 0.4876 1.3711 1.5150 0.5278 0.3604 0.3266 0.4070 1.4252 0.4674 0.1809 0.1132 0.0852 0.0703 0.0610 0.0546 0.0499 0.0461 0.0431 0.0405 0.0383
plot(ABS(1:50))

Jeffrey Clark on 14 Sep 2022
@Georges Theodosiou, you don't have enough samples to easily interpret the abs(fft), if you change Segm = 1:2048 to use 16384 you get
Your plot from 2048 samples shows that the second peak contains the energy over a wider frequency range. Instead of increasing the number of samples this can be captured by increasing the fft n-point DFT by adding 16384 as the DFT size e.g., ABS = (abs(fft(Xn,16384))) which results in
Jeffrey Clark on 21 Sep 2022
Edited: Jeffrey Clark on 21 Sep 2022
@Georges Theodosiou, I don't have a dsp, my intel cpu for 16384 points takes 2.83e-04 seconds using MATLAB's fft.
If the fft time for you is too long there is a way to estimate the actual peak from your 2048 fft, which only works if you know that the frequency of the signals being measured are stable and not chirped (as is the case for your test data). In essance you compute the area under the fft curve where the phase adjacent to the peaks' phase are related using unwrap(angle(fft)).
Georges Theodosiou on 28 Sep 2022
@Jeffrey Clark. Dear gentlemen, please le me express you my sincere gratitude for your kindness to help me, and tell you I'm beginner in DSP and MATLAB, also homeless (in France, though Greek). I get internet access in municipal Libraries and social Centers. My project, metrw-pitch, demands that user could see on screen his voice's pitch at least 8 times per second. Regards.