## Wavelet Coherence

Wavelet transform coherence (WTC) is a method for analyzing the coherence and phase lag between two time series as a function of both time and frequency (Chang and Glover 2010). Here I played with it using the MatLab toolbox provided by Grinsted et al.

In the following examples, I created two time series, x (blue) and y (red) with different properties (phase shift, frequency and amplitude) and run wtc(x,y,’mcc’,0) command. Small white noise was added to the time series.

1. Phase shift and angle. A rightward arrow indicates 0 lag; a bottom-right arrow indicates a small lead of x; a leftward arrow indicates x and y is anti-correlated.

2. Frequency. At what frequency (or period) are x and y correlated?

3. Amplitude. It seems amplitude doesn’t matter much.

Toolbox can be found:

~~http://www.pol.ac.uk/home/research/waveletcoherence/~~

**Note: this link is dead**. To download the “Cross Wavelet and Wavelet Coherence Toolbox”, please enter

http://www.alivelearn.net/?p=1561

Source code:

t =[1:1000]/10; %% effect of phase x = sin(t) + randn(size(t))/5; y = [sin(t(1:250)) sin(t(251:500)-pi/4) sin(t(501:750)-pi/2) sin(t(751:end)-pi)] + randn(size(t))/5; figure('color','w'); subplot(2,1,1); wtc(x,y,'mcc',0) subplot(2,1,2); plot(x); hold on; plot(y,'r') %% effect of frequency x = [sin(2*t(1:250)) sin(2*t(251:500)) sin(4*t(501:750)) sin(8*t(751:end))] + randn(size(t))/5; y = [sin(2*t(1:250)) sin(2*t(251:500)) sin(4*t(501:750)) sin(8*t(751:end))] + randn(size(t))/5; figure('color','w'); subplot(2,1,1); wtc(x,y,'mcc',0) subplot(2,1,2); plot(x); hold on; plot(y,'r') %% effect of amplitude x = [sin(2*t(1:250)) sin(2*t(251:500)) sin(4*t(501:750)) sin(8*t(751:end))] + randn(size(t))/5; y = [sin(2*t(1:250)) sin(2*t(251:500))/2 sin(4*t(501:750))/3 sin(8*t(751:end))/4] + randn(size(t))/5; figure('color','w'); subplot(2,1,1); wtc(x,y,'mcc',0) subplot(2,1,2); plot(x); hold on; plot(y,'r')

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please help me about running wavelet coherence and cross wavelet programs

I have updated the toolbox, put it on github, and it is now hosted at: http://www.glaciology.net/wavelet-coherence

Dear Xu Cui,

Can we have wavelet coherence Matrix in Matlab?

Respected Sir,

I need an help from you.I have a doubt in wavelet coherence using matlab.i have two series of length 80.how should i write the code in matlab so that i will get the wavelet coherence of two time series is a single value?

HOW I UPDATED THE WAVELET TOOL BOX FOR PERFORMING THE CROSSWAVELET AND WAVELET COHERENCE

Your test is simulation experiment.How about truthful data

respected sir

I see that the arrows pointed up indicated the second series lag the first series 1/4 cycle on the site https://www.mathworks.com>examples