# Calculation of mean signal frequency

46 views (last 30 days)
Diogo Tecelão on 27 Jul 2020
Commented: Star Strider on 15 Sep 2022
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
Abhineet Ram on 15 Sep 2022
Hi, where did you get this formula? I would like to understand the concept of this method/code. Thanks

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 15 Sep 2022
@Abhineet Ram — Probably Wikipedia. (It’s been a few years.)
It would have been easier had I used and linked to the meanfreq function (introduced in R2015a, proving once again that reading the Release Notes is time well-spent, something I obviously did not spend enough time on), that I now refer you to.
The related medfreq function calculates the median frequency.