If I understand what LPC does, I think. It predicts the next sample by taking into account previous $p$ samples. I don't understand why it is useful in DPS and speech recognition.
I also came across LPCC that can be derived from LPC and are related to sound frequency. I also find it hard to follow the idea why cepstrum coefficients are useful or even better for speech recognition.
I did read about MFCC, though. I understood that before DCT, the coefficients (no MFCC yet) are simply energies at particular frequency range of a signal that is filtered by a triangle band pass filter. I do not have a problem with MFCC apart from the last step when DCT is applied. I think it also has something to do with cepstrum.
Why do you think cepstrum is so useful for speech, speaker and music recognition?
I'd be grateful for some words on that :)
EDIT. I have found a typo. Instead of "I have a problem with MFCC apart from at the last step when DCT is applied" I really meant "I do not have a problem with MFCC apart from the last step when DCT is applied".
Could someone please add a tag "LPCC" to this topic? It is one of the techniques in speech I think and deserves to be tagged. I cannot do it at the moment. Cheers!