# Calculation of mean signal frequency

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Diogo Tecelão on 27 Jul 2020
Commented: Star Strider on 27 Jul 2020
Hi everyone,
I'm trying to perform an analysis in the frequency domain, but I'm confused regarding how to obtain the PSD signal.
Currently, I'm using the following to obtain the PSD:
L = length(data);
% Compute Fast Fourier Transform
Y = fft(data);
% Compute the two-sided spectrum P2
P2 = abs(Y/L);
% Compute the single-sided spectrum P1 based on P2
P1 = P2(1:ceil(L/2)+1);
P1(2:end-1) = 2*P1(2:end-1);
power = P1;
% Define the frequency domain axis
frequencies = fs*(0:ceil(L/2))/L;
I have tested this with the following signal:
fs = 200;
x = 0:1/fs:20
data = sin(2*pi*5*x);
And I get the following PSD: I'm trying to calculate the mean frequency using the following formula:
mean_frequency = sum(power.*frequencies)/sum(frequencies)
Where I obtain
mean_frequency = 5.0587e-04
which is obviously wrong. However, when I use MATLAB's meanfreq function, I get meanfreq(data, fs) = 4.999Hz, which is the expected.
Can please anyone tell me what I'm doing wrong? After this I want to perform a complete analysis in the frequency domain (e.g, median frequency, total power, etc) and I need to make sure my PSD data is correct.
Diogo

Star Strider on 27 Jul 2020
There are two small errors.
Correcting them:
P2 = abs(Y/L).^2; % Power = Amplitude^2
and:
mean_frequency = sum(power.*frequencies)/sum(power) % Divide By Sum Of Power
producing:
meanfreq =
4.99913568484097
.
Star Strider on 27 Jul 2020
Anything I could recommend would be limited only to my experience.
A much better option would be the MathWorks Academia site For Students, and particularly, Books.
(My personal preference for books is Alibris.)