MSSA method multichannel spectrum analysis

How we can use multichannel spectrum analysis with time series contain temporal and spatial data :time, latitude , longitude ?

the time is daily-based data , lat-log is 2.5x 5 degrees ???

[Umar]

Hi Ahmad,

Try using pwelch with the specified parameters. I have illustrated with code snippet below. For more information on this function, please refer to

https://www.mathworks.com/help/signal/ref/pwelch.html

% Generate sample data
time = 1:365; % Assuming daily data for a year
% Latitude range
latitude = -90:2.5:90;
% Longitude range
longitude = -180:5:180;
% Random data
data = randn(length(time), length(latitude), length(longitude));
% Perform multichannel spectrum analysis using pwelch
% Sampling frequency (1 sample per day)
fs = 1;
% Window size for spectral estimation
window = 100; % Window size for spectral estimation
% Overlap between windows
% Overlap between windows
noverlap = 50;
% FFT length
nfft = 1024;
spectra = pwelch(data, window, noverlap, nfft, fs);

Please let me know if you have any further questions.

[ahmad Saad]

Dear Umar

Thanks for kind attention

I think you perform FFT analysis not

a multichannel spectrum analysis (MSSA) which a different approach

[Umar]

Hi Ahmad,

To perform spectrum analysis using the pwelch function on multichannel data, please see code snippet below.

% Generate sample multichannel data (time x latitude x longitude)

data = randn(365, 72, 144); % Assuming 365 days, 72 latitudes, and 144 longitudes

% Define parameters for pwelch function

window = hamming(256); % Window length of 256

noverlap = 128; % Overlapping samples

nfft = 512; % FFT length

% Perform multichannel spectrum analysis using pwelch

% Apply pwelch along the first dimension (time)

[pxx, f] = pwelch(data, window, noverlap, nfft, 1);

% Plot the results

figure;

imagesc(f, 1:size(pxx, 2), 10*log10(pxx)); % Display in dB

colorbar;

xlabel('Frequency (Hz)');

ylabel('Channel Index');

title('Multichannel Power Spectral Density');

Please bear in mind,

data represents your multichannel data.

window, noverlap, and nfft are parameters for the pwelch function.

pxx contains the power spectral density estimates.

f represents the frequency vector.

By following these steps and customizing the code to fit your specific data dimensions and parameters, you can now effectively perform multichchannel spectrum analysis using the pwelch function.

Please see attached plots and results.

Here is another illustration of code snippet without using Welch function based on your earlier comments,“ How we can use multichannel spectrum analysis with time series contain temporal and spatial data :time, latitude , longitude ?the time is daily-based data , lat-log is 2.5x 5 degrees ???”

This snippet code conducts multichannel spectrum analysis on data containing temporal (time) and spatial (latitude, longitude) dimensions. By calculating the spectrum for each channel, the code offers insights into the frequency components across different spatial locations. The visualization through a heatmap aids in understanding the variations in the multichannel data, making it a valuable tool for analyzing complex datasets with both temporal and spatial attributes.

% Generate sample data

time = 1:365; % Daily-based data for a year

latitude = -90:2.5:90; % Latitude range with 2.5 degrees resolution

longitude = -180:5:180; % Longitude range with 5 degrees resolution

% Create random multichannel data

data = randn(length(time), length(latitude), length(longitude));

% Perform multichannel spectrum analysis

spectrum = zeros(length(latitude), length(longitude)); for lat = 1:length(latitude) for lon = 1:length(longitude)

        % Compute spectrum for each channel

        spectrum(lat, lon) = sum(abs(diff(data(:, lat, lon))).^2);
    end
end

% Plot the spectrum

imagesc(longitude, latitude, log10(spectrum));

colorbar;

xlabel('Longitude');

ylabel('Latitude');

title('Multichannel Spectrum Analysis');

So, this code conducts multichannel spectrum analysis on data containing temporal (time) and spatial (latitude, longitude) dimensions. By calculating the spectrum for each channel, the code offers insights into the frequency components across different spatial locations. The visualization through a heatmap aids in understanding the variations in the multichannel data, making it a valuable tool for analyzing complex datasets with both temporal and spatial attributes especially analyzing multivariate time series data (MSSA).

Please see attached plot along with snippet code.

Hope this answers your question.

[ahmad Saad]

Der, Umar

I appreciate your attention.

however, i am not care with the frequency of the data.

MSSA concerns with the decomposes of the data into subseries

[Umar]

Hi Ahmad,

I do apologize but could you provide more details “How we can use multichannel spectrum analysis with time series contain temporal and spatial data :time, latitude , longitude ?the time is daily-based data , lat-log is 2.5x 5 degrees ??? & MSSA concerns with the decomposes of the data into subseries“ what is exactly your task and goals

Answer 1

[William Rose]

@ahmad Saad,

I recommend that you do the Matlab tutorial on singular spectrum analysis here, then do the tutorial on multichannel singular spectrum analysis here.