Power Spectral Density Question

Consider a four-input, one-output nonlinear system, say an amplifier.

I have available the four power spectral density (PSD) curves for the
four pseudo-random input signals, and also the PSD, P(f), of the
output signal, where the independent variable f is frequency.

I would like to know if it is possible to determine the amount of
power present in the output signal that is due to nonlinear effects. 
So I would like to obtain the decomposition (if it even makes sense)
   P(f) = P_1(f) + P_2(f) + P_3(f) + P_4(f) + Q(f)
where P_k is the power due to linear amplification of the k'th input
signal, and Q(f) is the power present in the output signal which is
the sum of the noise contribution and all intermodulation products.

Is it possible to do this?  Is there an efficient algorithm?  The PSDs
are sampled at about 20000 discrete frequencies.

Thanks,
Peter

Peter Simon wrote:
> Consider a four-input, one-output nonlinear system, say an amplifier.
> 
> I have available the four power spectral density (PSD) curves for the
> four pseudo-random input signals, and also the PSD, P(f), of the
> output signal, where the independent variable f is frequency.

Can you measure the ouput PSD of each of the four input signals seperately?