wavelet coherence significance test

I am using wcoherence to get the wavelet coherence of two signals.

how can i evaluate the significance (eg. 95%) ??

[Saeed Soleimani]

You should use R programming language :-(

Answer 1

[Prasanna]

Hi yx,

To evaluate the significance of wavelet coherence when using the ‘wcoherence’ function in MATLAB, refer the following:

• First, compute the wavelet coherence between your two signals using the ‘wcoherence’ function.
• Create surrogate data to estimate the significance level. Surrogate data can be generated by randomizing one of the signals while preserving its power spectrum.
• Calculate the wavelet coherence for each surrogate dataset.
• Use the distribution of coherence values from the surrogate data to determine the significance threshold (e.g., the 95th percentile).

A sample MATLAB code to evaluate is as below assuming two example random signals:

% Example signals
x = randn(1, 1000);
y = randn(1, 1000);

% Compute wavelet coherence
[wcoh, ~, ~, ~] = wcoherence(x, y);

% Number of surrogates
numSurrogates = 1000;
surrogateCoherence = zeros(size(wcoh, 1), size(wcoh, 2), numSurrogates);

% Generate surrogate data and compute coherence
for i = 1:numSurrogates
    ySurrogate = y(randperm(length(y))); % Randomize y
    [wcohSurrogate, ~, ~, ~] = wcoherence(x, ySurrogate);
    surrogateCoherence(:, :, i) = wcohSurrogate;
end

% Determine the 95th percentile threshold
significanceThreshold = prctile(surrogateCoherence, 95, 3);

% Plot the wavelet coherence and significance threshold
figure;
subplot(2, 1, 1);
imagesc(wcoh);
title('Wavelet Coherence');
colorbar;

subplot(2, 1, 2);
imagesc(significanceThreshold);
title('95% Significance Threshold');
colorbar;

The output of the above sample code is as follows:

The surrogate data is generated by randomizing one of the signals. This helps in creating a distribution of coherence values under the null hypothesis. For more information regarding the functions used, refer the following documentations:

• wcoherence: https://www.mathworks.com/help/wavelet/ref/wcoherence.html
• prctile: https://www.mathworks.com/help/matlab/ref/prctile.html