Unitary Matrix Generation Question

Hello,
I have a question about how to generate 2x2 unitary matrices (for a 2 source
2 sensor ICA problem).

As we all know, one of the popular ICA techniques is to (eg, Jade)
- first whiten the data
- Next, apply an unitary matrix, that makes the components independent.

I have a way to evaluate "amount of independence" (This is my "cost"
function) of the separated components, given an unitary matrix.

For real data, when unitary matrix = orthogonal matrix, I solve for an
optimization problem that maximizes the cost. The
optimization is done over \theta, the orthogonal matrix
being the trivial one made of sines and cosines. The results of ICA I get
are very good.

Now, in the complex case, I have to similarly generate unitary
matrices. The question is, what is the parametric form of unitary
matrices? i.e, just like I needed theta (1 parameter) to generate
a 2x2 orthogonal matrix, how many parameters I need to generate
an unitary matrix, and what is the formula relating the unitary matrix
and these parameters.

Please resond at: wei_tan70_at_hotmail.com
Regards,

Wei

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Received on Thu Nov 30 17:05:57 2000