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Calculation of mean signal frequency

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Diogo Tecelão
Diogo Tecelão 2020-7-27
评论： Star Strider 2022-9-15
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.
Many thanks for your attention,
Diogo
  1 个评论
Abhineet Ram
Abhineet Ram 2022-9-15
Hi, where did you get this formula? I would like to understand the concept of this method/code. Thanks

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Star Strider
Star Strider 2020-7-27
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
.
  6 个评论
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Abhineet Ram
Abhineet Ram 2022-9-15
Hi, where did you get this formula? I would like to understand the concept of this method/code. Thanks
Star Strider
Star Strider 2022-9-15
@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.

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