The cross-correlation function (CCF) is a measure of the similarity between two time series as a function of the time lag between them. It is calculated by taking the dot product of the two time series after one of them has been shifted by a certain lag. The lag at which the CCF is maximized is interpreted as the time lag between the two time series at which they are most similar.

To calculate the CCF in MATLAB, you can use the xcorr() function. This function takes two time series as input and returns the CCF between them as output. The syntax for the xcorr() function is as follows:

Code snippet

[ccf, lags] = xcorr(x, y, maxlag, scaleopt)

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where:

• x and y are the two time series to be correlated
• maxlag is the maximum lag to consider (optional)
• scaleopt is a string that specifies the normalization option for the CCF (optional)

The ccf output argument contains the CCF between the two time series. The lags output argument contains the lags at which the CCF was calculated.

To calculate the CCF between two points in a flow over a cylinder simulation, you can use the following steps:

The following MATLAB code shows how to calculate the CCF between two points in a flow over a cylinder simulation:

Code snippet

% Load the flow over a cylinder simulation data load('flow_over_cylinder.mat'); % Extract the velocity time series at the two points of interest P1 = velocity(:, 1); P2 = velocity(:, 10); % Calculate the CCF between the two velocity time series [ccf, lags] = xcorr(P1, P2); % Plot the CCF as a function of the lag figure; plot(lags, ccf); xlabel('Lag (samples)'); ylabel('Cross-correlation'); title('Cross-correlation between two points in a flow over a cylinder simulation');

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This code will produce a plot of the CCF between the two velocity time series. The peak of the CCF will correspond to the time lag at which the two velocity time series are most similar.

If you are not seeing the expected results, it is important to check the following:

• Make sure that the velocity time series are at the same sampling frequency.
• Make sure that the velocity time series are detrended before calculating the CCF.
• Make sure that the maxlag parameter is set to a sufficiently large value.
• Make sure that the scaleopt parameter is set to the appropriate normalization option.

If you are still having problems, please provide more information about your specific setup, including the code that you are using and the data that you are working with.

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Ensure that your signal data (P1 and P2) is preprocessed appropriately. This might involve removing any trends or averaging to get better stationary time series.As you mentioned, you've collected data after 150 vortex-shedding cycles. Make sure you're segmenting the signals in an appropriate manner to perform the cross-correlation analysis. If you want to exclude any initial transients, ensure they're not included in the analysis.Normalize the signals to ensure that their magnitudes don't affect the correlation computation.Use the xcorr function in MATLAB, but ensure you correctly set the maximum lag parameter (maxlag) according to your data's nature and sampling frequency. for instance: % Assuming P1 and P2 are your velocity signals at two different points % Remove mean and normalize signals P1 = detrend(P1, 'constant'); P2 = detrend(P2, 'constant'); P1 = P1 / norm(P1); P2 = P2 / norm(P2); % Calculate cross-correlation [correlation, lag] = xcorr(P1, P2, 'coeff'); % Plot the cross-correlation plot(lag, correlation); xlabel('Lag'); ylabel('Cross-correlation'); title('Cross-correlation between P1 and P2');

i hope i helped.

Hi Dimitrios Sargiotis, thank you for your kind response. I tried to follow up your suggestions but I am still not getting what I expect...

I attached a picture of what I am getting

Thank you.

You may perform cross-correlation by FFT check out the link below:

https://www.mathworks.com/matlabcentral/fileexchange/53570-xcorr2_fft-a-b