9.3.4 Mel filter bank and log

The results of the FFT will be information about the amount of energy at each frequency band. Human hearing, however, is not equally sensitive at all frequency bands. It is less sensitive at higher frequencies, roughly above 1000 Hertz. It turns out that modeling this property of human hearing during feature extraction improves speech recognition performance. The form of the model used in MFCCs is to warp the frequencies output by the DFT onto the mel scale mentioned in Ch. 7. A mel (Stevens et al., 1937; Stevens and Volkmann, 1940) is a unit of pitch defined so that pairs of sounds which are perceptually equidistant in pitch are separated by an equal number of mels. The mapping between frequency in Hertz and the mel scale is linear below 1000 Hz and the logarithmic above 1000 Hz. The mel frequency m can be computed from the raw acoustic frequency as follows:

$$ mel(f)=1127\ln(1+\frac{f}{700}) $$

During MFCC computation, this intuition is implemented by creating a bank of filters which collect energy from each frequency band, with 10 filters spaced linearly below 1000 Hz, and the remaining filters spread logarithmically above 1000 Hz. Fig. 9.13 shows the bank of triangular filters that implement this idea.

Finally, we take the log of each of the mel spectrum values. In general the human response to signal level is logarithmic; humans are less sensitive to slight differences in amplitude at high amplitudes than at low amplitudes. In addition, using a log makes the feature estimates less sensitive to variations in input (for example power variations due to the speaker's mouth moving closer or further from the microphone).