Question about LPC analysis and noise suppression in speech

Hello,

I conducted an experiment in MATLAB related to noise suppression.

I have a noisy speech segment X=S+N where S is clean speech and N is
noise.

I did LPC analysis of a frame of X and obtained an estimate of a noisy
excitation (residual) signal u_noisy.

I also did LPC analysis of a frame of S and obtained an estimate of a
clean excitation signal u_clean.

I then filtered u_noisy with the LPC-coefficients from the LPC-analysis
of the clean speech frame.

I also filtered u_clean with the LPC-coefficients from the LPC-analysis
of the noisy speech frame.

Result:
The experiment showed that having clean LPC coefficients doesn't really
make a big difference. What makes a big difference is if you have a clean
residual signal.

So I am wondering if my results are correct? Or did I oversee something?