# spectral coherence between several time series

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Richard on 30 Jul 2012
I need some advice regarding the spectral coherence of several signals. Consider the following example:
t = 1:365;
A = 1;
f = 24;
fs = 1/f;
y = A.*sin(2.*pi.*fs.*t);
Data = y + rand(1,length(t));
depth = 1:9;
for i = 1:10;
data(i,:) = Data+rand(1,length(t));
% spectral analysis
[Pxx(i,:),F(i,:)] = periodogram(data(i,:),rectwin(length(data(i,:))),length(data(i,:)),1);
end
figure(1);
subplot(2,1,1);
plot(F(1,:),10.*log10(Pxx(1,:)));
subplot(2,1,2);
This example shows the spectra for air temperature as subplot(211) and then the spectra for the temperature at each depth in a water column in subplot(212). However, I would like to calculate the coherence in the spectra (if this makes sense), showing that the coherence between air temperature and water temperature decreases with depth in the water column. Can anyone suggest a method for this? Or any advice on this matter.

Wayne King on 30 Jul 2012
I'll assume you really want to add Gaussian noise and not uniform noise to the data.
y = A.*sin(2*pi*1/T*t);
Data1 = y + randn(1,length(t));
Data2 = y+randn(1,length(t));
[Cxy,W] = mscohere(Data1,Data2,hamming(96),48,96,1);
plot(W,Cxy);

Wayne King on 30 Jul 2012
You want to use mscohere.m to compute the magnitude squared coherence between two time series
Richard on 30 Jul 2012
could you provide an example of the most appropriate way of using mscohere for the example shown?

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