How is the orthogonalization symmetric in the "bst_henv.m" function?

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Hi @gvh,

The two orthogonalizations happen in

Xext    = repmat(tXh,1,nSig) ;
Yext    = repelem(tXh,1,nSig) ;    
Yext_p  = imag(bsxfun(@times, Yext, conj(Xext)./abs(Xext)));

This operation is performed for each band, we can let aside the frequency dimension for now. Consider two (column vector) signals u and v with their corresponding analytic signals [ũ, ṽ], and the variable tXh containing those signals, this is to say: tXh = [ũ, ṽ]

Then, Xext is equal to [ũ, ṽ, ũ, ṽ] , and Yext is equal to [ũ, ũ, ṽ, ṽ] .
The operation is performed for each column vector, thus: Yext_p = [ũ⟂ũ, ũ⟂ṽ, ṽ⟂ũ, ṽ⟂ṽ]. Lastly, the correlation is computed and reshaped in

CorrMat = reshape(diag(corrFcn(abs(Xext),abs(Yext_p))),nSig,nSig) ;

In this case, CorrMat is a [2×2] matrix with:
[corr(|ũ|, |ũ⟂ũ|), corr(|ṽ|, |ũ⟂ṽ|) ; corr(|ũ|, |ṽ⟂u|), corr(|ṽ|, |ṽ⟂ṽ|)]

The average happens later in the line:

A(:,:,t,f) = (abs(CorrMat) + abs(CorrMat'))/2 ;

Best,
Raymundo

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