LR Rabiner and RW Schafer, June 3

DRAFT: L. R. Rabiner and R. W. Schafer, June 3, 2009
8.7. CEPSTRUM DISTANCE MEASURES 485
log magnitude
group delay
5
0
LPC spectrum
Short−time Fourier spectrum
−5
0 1 2 3 4
15
10
5
0
(a) LPC and Short-Time Fourier Spectrum
(b) Liftered Group Delay Spectrum (s = 1)
τ = 5
τ = 30 τ = 5
τ = 15
τ = 30
−5
0 1 2 3 4
frequency in kHz
Figure 8.40: (a) Short-time Fourier transform and LPC spectrum (b) Liftered
group delay spectrum.
Itakura and Umezaki [7] tested the group delay spectrum distance measure
in an automatic speech recognition system. They found that for clean test
utterances, the difference in recognition rate was small for different values of s
when τ ≈ 5 although performance suffered with increasing s for larger values of
τ. This was attributed to the fact that for larger s the group delay spectrum
becomes very sharply peaked and thus more sensitive to small differences in
formant locations. However, in test conditions with additive white noise and
also with linear filtering distortions, recognition rates improved significantly
with τ = 5 and increasing values of the parameter s.
8.7.4 Mel-Frequency Cepstrum Coefficents
As we have seen, weighted cepstrum distance measures have a directly equivalent
interpretation in terms of log spectrum distance in the frequency domain. This
is significant in light of models for human perception of sound, which are based
upon a frequency analysis performed in the inner ear. With this in mind, Davis
and Mermelstein [2] formulated a new type of cepstrum representation that has
come to be widely used and known as the mel-frequency cepstrum coefficients
(mfcc).
The basic idea is to compute a frequency analysis based upon a filter bank
with approximately critical band spacing of the filters and bandwidths. For 4
kHz bandwidth, approximately 20 filters are used. In most implementations,