MEL-FREQUENCY CEPSTRUM
Recall our filterbank, which we construct in mel-frequency domain using a triangularly-shaped weighting function applied to mel-transformed log-magnitude spectral samples:


After computing the DFT, and the log magnitude spectrum (to obtain the real cepstrum), we compute the filterbank outputs, and then use a discrete cosine transform: to compute the mel-frequency cepstrum coefficients. Note that the triangular weighting functions are applied directly to the magnitude spectrum, and then the logarithm is taken after the spectral samples are averaged. The resulting coefficients are an approximation to the the cepstrum, and in reality simply represent an orthogonal and compact representation of the log magnitude spectrum.

We typically use 24 filterbank samples at an 8 kHz sampling frequency, and truncate the DCT to 12 MFCC coefficients. Adding energy gives us a total of 13 coefficients for our base feature vector.