How to decide the number of cepstral coefficients?

Question

For audio classification we are using cepstral coefficients, but how should I decide the number of coefficients?

Answer 1

From CMUSphinx FAQ:

There are various types of MFCC which differ by number of parameters, but not really different for accuracy (it might be a few percent worse or better).

The interpretation of MFCC (Roughtly introduced Alan V. Oppenheim and Ronald W. Schafer. From Frequency to Quefrency: A History of the Cepstrum. IEEE SIGNAL PROCESSING MAGAZINE) is not applicable as such, and the use of 12 or 13 coefficients seem to be due to historical reasons in many of the reported cases. The choice of the number of MFCCs to include in an ASR system is largely empirical. To understand why any specific number of cepstral coefficients is used, you could do worse than look at very early (pre-HMM) papers. When using DTW using Euclidean or even Mahalanobis distances, it quickly became apparent that the very high cepstral coefficients were not helpful for recognition, and to a lesser extent, neither were the very low ones. The most common solution was to “lifter” the MFCCs - i.e. apply a weighting function to them to emphasise the mid-range coefficients. These liftering functions were “optimised” by a number of researchers, but they almost always ended up being close to zero by the time you got to the 12th coefficient.

In practice, the optimal number of coefficients depends on the quantity of training data, the details of the training algorithm (in particular how well the PDFs can be modelled as the dimensionality of the feature space increases), the number of Gaussian mixtures in the HMMs, the speaker and background noise characteristics, and sometimes the available computing resources.