To find angular frequency and wave vector for time series data

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Ismita on 17 Feb 2024
Commented: Star Strider on 4 Mar 2024
if I have 10 set of time series data velocity componnts Vx, Vy and Vz with 5 minutes interval of time, how to find the angular frequency and wave vector using minimum variance method for those data? Thanks

Star Strider on 17 Feb 2024
From what I’ve been able to discover, the ‘minimum vairance method’ is a heirarchical clustering approach. MATLAB has a few ways to do that. See the documentation section on Hierarchical Clustering, linkage and related functions for details.
If you want to fit those data to a function instead (estimating the function’s parameters using the data to optimise them), that is an entirely different problem. MATLAB has a number of different ways to solve it.
Ismita on 4 Mar 2024
Thank you! I am doing as follows. I request your opinion if I am wrong! thanks again.
%eigen value find
n = length(speed_R);
speedxz = [Ux, Uz];
% Step 2: Compute the covariance matrix manually
mean_speedxz = mean(speedxz);
centered_speedxz = speedxz - mean_speedxz;
covariance_matrix = (centered_speedxz' * centered_speedxz) / (n - 1);
% Step 3: Calculate eigenvalues and eigenvectors manually
[eigenvectors, eigenvalues] = eig(covariance_matrix);
% Step 4: Select eigenvectors corresponding to significant eigenvalues
eigenvalues = diag(eigenvalues);
[sorted_eigenvalues, indices] = sort(eigenvalues, 'descend');
num_significant_eigenvalues = 1; % Assuming you want the first significant eigenvector
significant_index = indices(1:num_significant_eigenvalues);
significant_eigenvector = eigenvectors(:, significant_index);
% Step 5: Compute the wave vector (normalized eigenvector)
wave_vector = significant_eigenvector / norm(significant_eigenvector);
% Step 6: Compute wave vector components
kmx = wave_vector(1)
kmy = wave_vector(2)
kmz = wave_vector(3)
%km = sqrt(kmx^2 + kmy^2 +kmz^2)
% Step 7: Compute magnitude of the wave vector
km = norm(wave_vector);
Star Strider on 4 Mar 2024
I have no idea what you are doing or what your data are.
I would probably use the fft function to find the frequency in time-varying waveform data. (I asume the data are amplitude as a function of time.)
If you have defined a system (for example a control system) ot diferential equations describing it, the eigenvalues of the ‘A’ matrix will be the charactreristic (resonant) frequencies of the system. I would be hesitant to apply that to time-series data.
With a 5-minute (300 second) sampling interval, the sampling frequency is 0.2 cycles/minute (0.00333 ... Hz) and ths highest frequency you could estimate (the Nyquist frequency) would be 0.1 cycles/minute (0.00166 ... Hz).
.

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