spectral coherence between several time series

Question

Richard 2012-7-30

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https://ww2.mathworks.cn/matlabcentral/answers/44850-spectral-coherence-between-several-time-series

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);
pcolor(F(2:end,:),depth,Pxx(2:end,:));shading interp;axis ij

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.

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Answer 1

Wayne King 2012-7-30

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https://ww2.mathworks.cn/matlabcentral/answers/44850-spectral-coherence-between-several-time-series#answer_54936

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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);