Sinusoidal liftering in implementations of MFCC Some implementations of MFCC apply sinusoidal liftering as the final step in calculations of MFCC. It is claimed that speech recognition can be significantly improved. For instance, if $\text{MFCC}_i$ is a cepstral coefficient, and $w$ is a lifter, then
$$\widehat{\text{MFCC}_i}=w_i\text{MFCC}_i$$

is a liftered cepstral coefficient, where $w_i$ for sinusoidal liftering is defined as:

$$w_i=1+\frac{D}{2}\sin\Big(\frac{\pi i}{D}\Big)$$

When I look at the equation, I understand the sinusoidal function has a shape such that its maximum is in the middle and approaches to zero at edges. Therefore, cepstral vector's first and the last coefficients are is reduced to zero while the middle one is intact.

Why is liftering applied and how does it improve the speech recognition?
This paper$^1$ suggests:



that the reason is because the filtered versions give less weight to the higher coefficients which provide less discrimination than the lower ones.

That paper references this one$^2$ which shows the plot below indicating how the application of window reduces the variability.



References


K.K. Paliwal "DECORRELATED AND LIFTERED FILTER-BANK ENERGIES FOR ROBUST
SPEECH RECOGNITION"
B.H. Juang, L.R. Rabiner and J.G. Wilpon, "On the use of bandpass liftering in speech recognition", IEEE Trans. Acoust., Speech and Signal Processing Vol. ASSP-35, No. 7, pp. 947-954, July 1987.