finding the dominant frequency via fourier transform

Hi All,

I have been struggling to find the dominant frequency for a series of data that I have recorded in my experiments. Would be wonderful if you help me how to resolve my issue.

data series:

t=[40:0.1:300.2];

x=[6.54E-06
6.53E-06
6.52E-06
6.54E-06
6.58E-06
6.62E-06
6.65E-06
6.67E-06
6.67E-06
6.66E-06
6.65E-06
6.66E-06
6.69E-06
6.73E-06
6.75E-06
6.73E-06
6.69E-06
6.66E-06
6.65E-06
6.66E-06
6.66E-06
6.64E-06
6.61E-06
6.56E-06
6.51E-06
6.48E-06
6.46E-06
6.47E-06
6.47E-06
6.50E-06
6.53E-06
6.56E-06
6.55E-06
6.52E-06
6.52E-06
6.56E-06
6.62E-06
6.67E-06
6.69E-06
6.70E-06
6.71E-06
6.72E-06
6.74E-06
6.77E-06
6.80E-06
6.82E-06
6.83E-06
6.83E-06
6.82E-06
6.80E-06
6.77E-06
6.75E-06
6.76E-06
6.78E-06
6.77E-06
6.75E-06
6.73E-06
6.73E-06
6.76E-06
6.80E-06
6.83E-06
6.86E-06
6.87E-06
6.87E-06
6.86E-06
6.83E-06
6.83E-06
6.83E-06
6.83E-06
6.83E-06
6.83E-06
6.81E-06
6.79E-06
6.76E-06
6.74E-06
6.73E-06
6.72E-06
6.69E-06
6.65E-06
6.61E-06
6.57E-06
6.53E-06
6.49E-06
6.46E-06
6.45E-06
6.45E-06
6.44E-06
6.44E-06
6.44E-06
6.43E-06
6.43E-06
6.43E-06
6.42E-06
6.43E-06
6.43E-06
6.41E-06
6.41E-06
6.42E-06
6.41E-06
6.38E-06
6.33E-06
6.32E-06
6.33E-06
6.35E-06
6.36E-06
6.36E-06
6.33E-06
6.28E-06
6.23E-06
6.21E-06
6.20E-06
6.21E-06
6.24E-06
6.27E-06
6.30E-06
6.32E-06
6.32E-06
6.29E-06
6.26E-06
6.26E-06
6.28E-06
6.31E-06
6.32E-06
6.32E-06
6.33E-06
6.33E-06
6.32E-06
6.32E-06
6.34E-06
6.35E-06
6.37E-06
6.37E-06
6.34E-06
6.29E-06
6.24E-06
6.20E-06
6.19E-06
6.20E-06
6.22E-06
6.24E-06
6.24E-06
6.23E-06
6.22E-06
6.20E-06
6.18E-06
6.17E-06
6.19E-06
6.23E-06
6.27E-06
6.30E-06
6.31E-06
6.30E-06
6.30E-06
6.32E-06
6.35E-06
6.36E-06
6.37E-06
6.37E-06
6.38E-06
6.37E-06
6.37E-06
6.36E-06
6.37E-06
6.39E-06
6.40E-06
6.40E-06
6.40E-06
6.40E-06
6.37E-06
6.34E-06
6.29E-06
6.26E-06
6.24E-06
6.24E-06
6.23E-06
6.20E-06
6.17E-06
6.14E-06
6.13E-06
6.15E-06
6.19E-06
6.23E-06
6.27E-06
6.30E-06
6.32E-06
6.34E-06
6.33E-06
6.30E-06
6.27E-06
6.27E-06
6.28E-06
6.29E-06
6.31E-06
6.33E-06
6.35E-06
6.37E-06
6.41E-06
6.43E-06
6.44E-06
6.43E-06
6.39E-06
6.33E-06
6.27E-06
6.22E-06
6.19E-06
6.17E-06
6.18E-06
6.20E-06
6.23E-06
6.25E-06
6.27E-06
6.28E-06
6.29E-06
6.27E-06
6.26E-06
6.25E-06
6.25E-06
6.25E-06
6.27E-06
6.27E-06
6.26E-06
6.25E-06
6.22E-06
6.19E-06
6.17E-06
6.15E-06
6.15E-06
6.16E-06
6.18E-06
6.20E-06
6.20E-06
6.20E-06
6.19E-06
6.16E-06
6.13E-06
6.12E-06
6.12E-06
6.10E-06
6.08E-06
6.06E-06
6.06E-06
6.08E-06
6.12E-06
6.19E-06
6.24E-06
6.26E-06
6.26E-06
6.25E-06
6.22E-06
6.22E-06
6.22E-06
6.23E-06
6.25E-06
6.26E-06
6.27E-06
6.27E-06
6.27E-06
6.30E-06
6.34E-06
6.37E-06
6.39E-06
6.41E-06
6.41E-06
6.39E-06
6.37E-06
6.37E-06
6.38E-06
6.39E-06
6.38E-06
6.35E-06
6.33E-06
6.33E-06
6.33E-06
6.36E-06
6.39E-06
6.40E-06
6.40E-06
6.37E-06
6.34E-06
6.30E-06
6.27E-06
6.25E-06
6.25E-06
6.25E-06
6.25E-06
6.22E-06
6.20E-06
6.18E-06
6.19E-06
6.22E-06
6.26E-06
6.26E-06
6.24E-06
6.21E-06
6.18E-06
6.16E-06
6.17E-06
6.20E-06
6.24E-06
6.28E-06
6.32E-06
6.34E-06
6.34E-06
6.35E-06
6.36E-06
6.41E-06
6.46E-06
6.51E-06
6.53E-06
6.52E-06
6.49E-06
6.47E-06
6.48E-06
6.51E-06
6.56E-06
6.60E-06
6.60E-06
6.58E-06
6.53E-06
6.47E-06
6.42E-06
6.41E-06
6.42E-06
6.42E-06
6.39E-06
6.35E-06
6.29E-06
6.22E-06
6.16E-06
6.12E-06
6.11E-06
6.12E-06
6.13E-06
6.13E-06
6.12E-06
6.11E-06
6.11E-06
6.12E-06
6.15E-06
6.22E-06
6.30E-06
6.35E-06
6.36E-06
6.34E-06
6.33E-06
6.35E-06
6.38E-06
6.44E-06
6.49E-06
6.53E-06
6.54E-06
6.54E-06
6.52E-06
6.49E-06
6.47E-06
6.46E-06
6.45E-06
6.43E-06
6.41E-06
6.38E-06
6.35E-06
6.34E-06
6.36E-06
6.40E-06
6.44E-06
6.46E-06
6.46E-06
6.47E-06
6.48E-06
6.49E-06
6.50E-06
6.51E-06
6.53E-06
6.54E-06
6.53E-06
6.52E-06
6.52E-06
6.55E-06
6.60E-06
6.63E-06
6.66E-06
6.68E-06
6.70E-06
6.71E-06
6.71E-06
6.70E-06
6.69E-06
6.67E-06
6.64E-06
6.62E-06
6.62E-06
6.63E-06
6.65E-06
6.69E-06
6.73E-06
6.77E-06
6.80E-06
6.82E-06
6.82E-06
6.81E-06
6.81E-06
6.82E-06
6.81E-06
6.80E-06
6.79E-06
6.77E-06
6.77E-06
6.77E-06
6.76E-06
6.77E-06
6.76E-06
6.76E-06
6.75E-06
6.74E-06
6.73E-06
6.71E-06
6.68E-06
6.65E-06
6.64E-06
6.64E-06
6.62E-06
6.58E-06
6.51E-06
6.45E-06
6.40E-06
6.38E-06
6.38E-06
6.40E-06
6.42E-06
6.44E-06
6.46E-06
6.45E-06
6.44E-06
6.44E-06
6.43E-06
6.41E-06
6.40E-06
6.41E-06
6.42E-06
6.42E-06
6.41E-06
6.43E-06
6.46E-06
6.50E-06
6.53E-06
6.55E-06
6.54E-06
6.53E-06
6.53E-06
6.52E-06
6.51E-06
6.50E-06
6.48E-06
6.47E-06
6.47E-06
6.48E-06
6.48E-06
6.48E-06
6.47E-06
6.46E-06
6.45E-06
6.44E-06
6.43E-06
6.41E-06
6.41E-06
6.40E-06
6.40E-06
6.40E-06
6.40E-06
6.39E-06
6.37E-06
6.36E-06
6.37E-06
6.39E-06
6.41E-06
6.42E-06
6.42E-06
6.41E-06
6.37E-06
6.35E-06
6.33E-06
6.33E-06
6.35E-06
6.38E-06
6.39E-06
6.39E-06
6.38E-06
6.38E-06
6.37E-06
6.37E-06
6.39E-06
6.40E-06
6.41E-06
6.40E-06
6.38E-06
6.37E-06
6.35E-06
6.33E-06
6.33E-06
6.32E-06
6.31E-06
6.29E-06
6.25E-06
6.22E-06
6.22E-06
6.23E-06
6.25E-06
6.29E-06
6.32E-06
6.33E-06
6.32E-06
6.31E-06
6.30E-06
6.30E-06
6.32E-06
6.33E-06
6.34E-06
6.35E-06
6.36E-06
6.38E-06
6.40E-06
6.43E-06
6.45E-06
6.45E-06
6.44E-06
6.43E-06
6.41E-06
6.37E-06
6.32E-06
6.29E-06
6.30E-06
6.31E-06
6.33E-06
6.31E-06
6.27E-06
6.23E-06
6.21E-06
6.21E-06
6.22E-06
6.21E-06
6.19E-06
6.15E-06
6.12E-06
6.10E-06
6.08E-06
6.08E-06
6.09E-06
6.11E-06
6.15E-06
6.17E-06
6.18E-06
6.17E-06
6.15E-06
6.13E-06
6.14E-06
6.17E-06
6.20E-06
6.22E-06
6.22E-06
6.22E-06
6.21E-06
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6.20E-06
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6.20E-06
6.18E-06
6.17E-06
6.16E-06
6.16E-06
6.16E-06
6.16E-06
6.17E-06
6.18E-06
6.19E-06
6.20E-06
6.22E-06
6.25E-06
6.30E-06
6.34E-06
6.37E-06
6.38E-06
6.36E-06
6.31E-06
6.26E-06
6.24E-06
6.24E-06
6.28E-06
6.33E-06
6.38E-06
6.40E-06
6.39E-06
6.36E-06
6.33E-06
6.30E-06
6.30E-06
6.31E-06
6.30E-06
6.29E-06
6.26E-06
6.26E-06
6.26E-06
6.29E-06
6.33E-06
6.38E-06
6.40E-06
6.38E-06
6.35E-06
6.31E-06
6.27E-06
6.25E-06
6.26E-06
6.29E-06
6.33E-06
6.36E-06
6.37E-06
6.40E-06
6.44E-06
6.47E-06
6.50E-06
6.51E-06
6.54E-06
6.56E-06
6.58E-06
6.59E-06
6.61E-06
6.64E-06
6.66E-06
6.69E-06
6.71E-06
6.72E-06
6.74E-06
6.74E-06
6.73E-06
6.71E-06
6.69E-06
6.65E-06
6.61E-06
6.59E-06
6.59E-06
6.60E-06
6.60E-06
6.59E-06
6.57E-06
6.54E-06
6.52E-06
6.51E-06
6.50E-06
6.52E-06
6.55E-06
6.60E-06
6.60E-06
6.58E-06
6.55E-06
6.52E-06
6.51E-06
6.53E-06
6.56E-06
6.59E-06
6.61E-06
6.61E-06
6.60E-06
6.61E-06
6.63E-06
6.66E-06
6.69E-06
6.71E-06
6.73E-06
6.74E-06
6.72E-06
6.69E-06
6.67E-06
6.67E-06
6.70E-06
6.74E-06
6.77E-06
6.77E-06
6.75E-06
6.72E-06
6.71E-06
6.71E-06
6.71E-06
6.72E-06
6.72E-06
6.72E-06
6.73E-06
6.74E-06
6.73E-06
6.71E-06
6.69E-06
6.67E-06
6.67E-06
6.69E-06
6.70E-06
6.71E-06
6.72E-06
6.74E-06
6.76E-06
6.77E-06
6.75E-06
6.72E-06
6.70E-06
6.68E-06
6.68E-06
6.68E-06
6.68E-06
6.68E-06
6.68E-06
6.70E-06
6.72E-06
6.75E-06
6.79E-06
6.84E-06
6.89E-06
6.92E-06
6.95E-06
6.95E-06
6.94E-06
6.92E-06
6.91E-06
6.93E-06
6.96E-06
6.98E-06
6.98E-06
6.96E-06
6.93E-06
6.89E-06
6.85E-06
6.82E-06
6.81E-06
6.81E-06
6.78E-06
6.75E-06
6.71E-06
6.68E-06
6.65E-06
6.63E-06
6.61E-06
6.60E-06
6.60E-06
6.59E-06
6.55E-06
6.51E-06
6.47E-06
6.46E-06
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6.47E-06
6.46E-06
6.42E-06
6.36E-06
6.28E-06
6.23E-06
6.17E-06
6.13E-06
6.10E-06
6.08E-06
6.06E-06
6.06E-06
6.05E-06
6.06E-06
6.08E-06
6.11E-06
6.12E-06
6.11E-06
6.08E-06
6.04E-06
5.99E-06
5.97E-06
5.98E-06
6.01E-06
6.04E-06
6.05E-06
6.03E-06
6.02E-06
6.00E-06
5.98E-06
5.96E-06
5.95E-06
5.95E-06
5.95E-06
5.93E-06
5.90E-06
5.87E-06
5.85E-06
5.83E-06
5.82E-06
5.82E-06
5.83E-06
5.84E-06
5.85E-06
5.87E-06
5.90E-06
5.92E-06
5.92E-06
5.90E-06
5.89E-06
5.91E-06
5.94E-06
5.95E-06
5.95E-06
5.93E-06
5.92E-06
5.92E-06
5.92E-06
5.94E-06
5.96E-06
5.97E-06
5.98E-06
6.00E-06
6.01E-06
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6.00E-06
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6.02E-06
6.04E-06
6.04E-06
6.01E-06
5.97E-06
5.94E-06
5.93E-06
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5.93E-06
5.94E-06
5.95E-06
5.96E-06
5.98E-06
6.02E-06
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5.98E-06
5.94E-06
5.92E-06
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6.00E-06
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6.07E-06
6.07E-06
6.05E-06
6.02E-06
6.00E-06
5.98E-06
5.97E-06
5.99E-06
6.02E-06
6.06E-06
6.09E-06
6.11E-06
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6.12E-06
6.14E-06
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6.11E-06
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6.02E-06
6.01E-06
6.05E-06
6.09E-06
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6.07E-06
6.03E-06
6.00E-06
5.98E-06
5.96E-06
5.95E-06
5.97E-06
5.99E-06
6.00E-06
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5.99E-06
5.97E-06
5.94E-06
5.91E-06
5.88E-06
5.86E-06
5.85E-06
5.83E-06
5.81E-06
5.80E-06
5.84E-06
5.89E-06
5.93E-06
5.94E-06
5.96E-06
5.97E-06
5.97E-06
5.97E-06
5.97E-06
5.97E-06
5.98E-06
6.00E-06
6.04E-06
6.10E-06
6.17E-06
6.22E-06
6.24E-06
6.25E-06
6.27E-06
6.29E-06
6.29E-06
6.30E-06
6.32E-06
6.35E-06
6.38E-06
6.41E-06
6.41E-06
6.41E-06
6.41E-06
6.41E-06
6.40E-06
6.38E-06
6.36E-06
6.36E-06
6.38E-06
6.39E-06
6.41E-06
6.43E-06
6.42E-06
6.42E-06
6.44E-06
6.45E-06
6.45E-06
6.45E-06
6.44E-06
6.42E-06
6.41E-06
6.40E-06
6.39E-06
6.38E-06
6.37E-06
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6.37E-06
6.34E-06
6.32E-06
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6.31E-06
6.29E-06
6.26E-06
6.23E-06
6.21E-06
6.19E-06
6.18E-06
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6.22E-06
6.25E-06
6.28E-06
6.32E-06
6.38E-06
6.43E-06
6.47E-06
6.49E-06
6.46E-06
6.40E-06
6.33E-06
6.28E-06
6.26E-06
6.25E-06
6.26E-06
6.28E-06
6.32E-06
6.35E-06
6.35E-06
6.36E-06
6.37E-06
6.38E-06
6.39E-06
6.38E-06
6.34E-06
6.29E-06
6.25E-06
6.24E-06
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];

Fs = 10;                    % Sampling frequency
T = 0.1;                     % Sample time
L = length(t);                     % Length of signal
subplot(2,1,1);
plot(x);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);

NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(x,NFFT)/L;
f = Fs*linspace(0,1,NFFT);
subplot(2,1,2);
plot(f,Y) 
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')

This result doesn't seem to be right. Because this dominant frequency is physically meaningless! Can anyone help me to figure this issue? Many thanks in advance. Hadi

[Image Analyst]

"Undefined function or variable 'torque'."

Please give us code that runs so we can help you.

[Hadi Mohammadi]

ooops, please replace the "torque" with "x" in code.

%Y = fft(torque,NFFT)/L;

should be replaced by

Y = fft(x,NFFT)/L;

The rest of the code remains the same. thanks --H

[Azzi Abdelmalek]

x is not used in your code

[Image Analyst]

OK - I edited your original question and fixed it. But it doesn't look anything like a sine wave to me. But anyway, you have the FFT so you have the strength of all the sine waves that comprise your signal. You have them all - pick the first one if you want.

[Hadi Mohammadi]

@ Azzi: x is the "input" data and t is the recording time.

@ image analyst: Sorry, I didn't quite get your point. What do you mean by picking up the first one? Can you please elaborate more on this?

[Image Analyst]

If you need a tutorial on Fourier transforms, I have some links. But just briefly, just like you can construct any weird shaped curve or function as a sum of powers of x (this is the "Taylor series expansion"), you can also construct that curve out of a series of sine waves of frequencies that are multiples of each other. So a sine wave is An * sin(2 * pi * n * omega * x) where (n*omega) is the frequency of that sine wave. You'll have a bunch of them - lots and lots of sine waves. It takes many, many sine waves all added up with various weighting factors to create an arbitrary signal that you give it. So, which since wave do you want? There are many of them? And all of them have different weights which represent the amplitude (power, strength) of that particular sine wave. How do you define the "dominant" one? I would guess it's the one with the greatest amplitude. Since generally FFT's are large at 0 frequency and fall off as you go to higher and higher frequencies, that's why I suggested the first harmonic. You don't want the one at 0 frequency because that just represents the offset above zero (the mean of the signal) and it's not really a sine wave - it's a constant (or a sine wave of infinite period and zero frequency). But the first one will be the first harmonic and often that has the highest strength but not always, especially not for signals that are really periodic.

[Hadi Mohammadi]

Thanks for your through comment. I don't have much background on this field. But, have been reading and watching several things today and am much more familiar to the topic since yesterday. Just one last question; by first harmonic you mean the first peak after Hz = 0 or sth else? thanks again

[Image Analyst]

Harmonic means the first element. Second harmonic is the second element which is at twice the frequency of the first harmonic. The third harmonic is in the third element and has 3 times the frequency. These may or may not be a peak depending on what the original signal was.

Answer 1

[Youssef Khmou]

Your data is sampled with Fs=10 Hz, Your Frequency spectrum is :

 Fs=10;
 N=length(x);
 fx=fft(x)/N;
 f=(0:N-1)*Fs/N;
 figure, plot(f(1:end/2),10*log10(abs(fx(1:end/2))))

[Hadi Mohammadi]

Thanks Youssef for your response.

There is still one question that remains to be answered; which frequency is the dominant one? It appears that at Hz = 0, frequency is dominant which is totally meaningless! I'd appreciate it, if you give me your thoughts on this.

[Youssef Khmou]

Mohammadi, It is clear that the dominant frequency is 0 Hz, repeat the experiment, and analyse the data for second time for verification, try to verify if your data needs some pre-processing like filtering low, high, or bandpass, or verify the devices for some adjustment .

[Image Analyst]

Evidently Hadi didn't understand my explanation above about how all frequencies are present at various strengths, so here are some links: http://www.cv.nrao.edu/course/astr534/FourierTransforms.html

http://blogs.mathworks.com/steve/category/fourier-transforms/

http://www.mathworks.com/matlabcentral/fileexchange/28810-fourier-transform-demonstration/content/fourier_demo/html/fourier_demo.html