Formula to calculate Cepstral coefficients (not MFCC)

1. How many coefficients does MFCC have?
2. Why DCT is used in MFCC?

How many coefficients does MFCC have?

Traditional MFCC systems use only 8–13 cepstral coefficients. The zeroth coefficient is often excluded since it represents the average log-energy of the input signal, which only carries little speaker-specific information.

Why DCT is used in MFCC?

DCT is the last step of the main process of MFCC feature extraction. The basic concept of DCT is correlating value of mel spectrum so as to produce a good representation of property spectral local. Basically the concept of DCT is the same as inverse fourier transform.