Alberto, the question is not clear. When you say "in the time domain" do you mean you are looking for alternatives to the widely used perceptual audio coders that use filterbanks?
If "a spectral-weighted temporal approximation method" is what you want, don't try to "connect frequency components to specific samples in the time domain". Frequency components are not a relevant concept in the time domain.
Possibly what you want is something like LPC whitening with residual coding. See for example:Singhal, Sharad. "High quality audio coding using multipulse LPC." ICASSP, 1990.