How to extract the common part between two audio signals and remove it from the signal?

Question

If I have two audio signals Y1 and Y2 in Fourier domain that are the results of multiplication of S with H1 and H2 respectively (convolution in time domain):

Y1=H1*S

Y2=H2*S

And I don't have S and H1, H2, but I know that S is the same in both Y1 and Y2. Is there a good way to extract S out to only have H1 and H2 in the right side of the equation?

thanks

Answer 1

Looks like two equations with three variables. I don't think that you can extract the original signal, S.

Answer 2

I was asking myself the same question. My first approach was to do a crosscorellation between the signals, to get the point where they are most similar. then I padded one of the two so they are exactly "time synchronous", meaning the main sound source was exactly centered. I then substracted the one from the other. I think this is a valid approach, although I didn't follow through on it and its not working properly. If youve got additional ideas, let me know ;)