Hi uzzi
Here is how you can use the Prony's method to design a filter to find the external frequency and damping values.
- Import your data from the Excel file into MATLAB.
- Ensure your data is centered around zero if necessary and remove any trends or noise.
- Apply Matrix Pencil or Prony's Method. Both methods are used for estimating the parameters of a sum of damped sinusoids.
- Check how many frequencies are close to the fundamental frequency of 50 Hz and identify additional frequencies.
- Analyze the damping values corresponding to each frequency.
- Plot the original and reconstructed signals to verify the decomposition.
Here is a basic implementation using Prony's method.
% Load data from Excel
[data, txt, raw] = xlsread('filename.xlsx');
% Assume the first column is time and the second column is frequency
time = data(:, 1);
frequency = data(:, 2);
% Detrend the data
frequency = detrend(frequency);
% Define the order of the model (number of damped sinusoids)
modelOrder = 10; % Adjust based on your data
% Use Prony's method
[a, g] = prony(frequency, modelOrder, modelOrder);
% Calculate poles
poles = roots(a);
% Calculate frequencies and damping factors
frequencies = abs(angle(poles)) / (2 * pi * mean(diff(time)));
damping = -log(abs(poles)) / mean(diff(time));
% Display results
disp('Frequencies:'); disp(frequencies);
disp('Damping values:'); disp(damping);
% Reconstruct the signal
reconstructed_signal = zeros(size(frequency));
for k = 1:length(poles)
reconstructed_signal = reconstructed_signal + g(k) * exp(poles(k) * time);
end
% Plot
figure;
subplot(2, 1, 1);
plot(time, frequency);
title('Original Signal');
ylabel('Frequency');
subplot(2, 1, 2);
plot(time, real(reconstructed_signal));
title('Reconstructed Signal');
ylabel('Frequency');
Please refer to the following documentation links to learn more:
- detrend: https://www.mathworks.com/help/matlab/ref/detrend.html
- prony: https://www.mathworks.com/help/signal/ref/prony.html
Hope this helps!
