To calculate the percentage of wavelet coherence value and identify significant coherence regions, you can follow these steps using MATLAB. Wavelet coherence is a measure of the relationship between two signals in both time and frequency domains.
- Load your data: Load the two signals for which you want to calculate the wavelet coherence.
- Calculate Continuous Wavelet Transform (CWT):
- Use the Continuous Wavelet Transform to obtain the wavelet coefficients for both signals. You can use the cwt function in MATLAB to compute the CWT.
% Example code for CWT
[cwt_signal1, f_signal1] = cwt(signal1, 'amor', 'scal');
[cwt_signal2, f_signal2] = cwt(signal2, 'amor', 'scal');
Calculate the Cross-Wavelet Transform (XWT):
- Compute the cross-wavelet transform of the two signals.
% Example code for XWT
xwt = cwt_signal1 .* conj(cwt_signal2);
Calculate the Wavelet Coherence:
- Calculate the wavelet coherence using the XWT and individual wavelet transforms.
Identify Significant Coherence Regions:
- To find regions of significant coherence, you can perform a statistical test. One common approach is to compare the wavelet coherence values against a threshold derived from a significance test, such as a chi-squared test or bootstrapping. The threshold should be chosen based on your significance level (alpha).
% Example code for finding significant coherence regions
% Set the threshold based on a chi-squared test
chi2_threshold = chi2inv(1 - alpha, 2); % 2 degrees of freedom
significant_regions = wcoherence > chi2_threshold;
Calculate the Percentage of Significant Coherence:
- Calculate the percentage of significant coherence values relative to the total number of data points.
percentage_significant = sum(significant_regions(:)) / numel(significant_regions) * 100;
The percentage_significant will give you the percentage of the wavelet coherence values that are statistically significant according to your chosen alpha level.
