MFCC Features - Robust Emotion Recognition Using Spectral and Prosodic Features - page 108

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

Fig. A.1 Mel-filter bank

8
<

0 ; k\f ð m 1 Þ

ð ð Þ
f ð m Þ f ð m 1 Þ ;

2 k fm 1

f ð m 1 Þ k f ð m Þ

H m ð k Þ¼

ð A : 5 Þ

:

2 f ð m þ 1 Þð Þ
f ð m þ 1 Þ f ð m Þ ;

f ð m Þ \k f ð m þ 1 Þ

0 ; k [ f ð m þ 1 Þ

with m ranging from 0 to M 1.
5. Discrete Cosine Transform (DCT): Since the vocal tract is smooth, the energy
levels in adjacent bands tend to be correlated. The DCT is applied to the
transformed mel frequency coefficients produces a set of cepstral coefficients.
Prior to computing DCT the mel spectrum is usually represented on a log scale.
This results in a signal in the cepstral domain with a que-frequency peak
corresponding to the pitch of the signal and a number of formants representing
low que-frequency peaks. Since most of the signal information is represented
by the first few MFCC coefficients, the system can be made robust by extracting
only those coefficients ignoring or truncating higher order DCT components
[ 1 ]. Finally, MFCC is calculated as [ 1 ]

;

c ð n Þ¼ X

M 1

pn ð m 0 : 5 Þ
M

log 10 s ð m Þ ð Þ cos n ¼ 0 ; 1 ; 2 ; :::; C 1 ð A : 6 Þ

m ¼ 0

where c ð n Þ are the cepstral coefficients and C is the number of MFCCs.
Traditional MFCC systems use only 8-13 cepstral coefficients. The zeroth