Understanding the pitch filter

[davlar1]

Can anyone explain from the pitch filtering from the arxiv related paper, i.e.: "the filtering is performed by computing X(k) + αP(k) and then renormalizing the resulting signal to have the same energy in each band as the original signal X(k)"
So P(k) is the windowed DFT of the pitch-delayed signal, α is band dependent.
Does P(k) just represent the energy due to the pitch component ? And X(k) is just the energy (ok, more precisely DFT coefficient) in that frequency bin, and so includes the pitch component and everything else ?