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How to combine correlated signals !?

Hi everybody

There are 11 signals:

  • S_main : The original signal

  • S1 ~ S10 : 10 signals that are correlated to S_main with different correlation coefficients (coeff1 ~ coeff10)

Now here's the question:

How can I combine signals S1, S2, ..., S10 in order to regenerate S_main !!?

Thanks a billion for your upcoming help.