# The logarithm Energy measure in Speech

I am studying the mel-frequency cepstral coefficient (MFCC) and have downloaded a pdf which is related to MFCC from this link. It is about the "ETSI ES 201 108"

ETSI ES 201 108 - Speech Processing, Transmission and Quality aspects (STQ); Distributed speech recognition; Front-end feature extraction algorithm; Compression algorithms

I am curious about the 4.2.5 Energy Measure

How can they calculate a floor that makes sure that the result is not less than -50? I don't know the reason why the result is not less than -50. Would you know why and explain for me?

$$\max\left\{\sum_i s^2(i),\epsilon\right\}\tag{1}$$
with some small constant $\epsilon$ (they suggest $\epsilon=2e-22$ which gives $\ln\epsilon\approx -50$) to prevent the energy to become too small. The reason for this is that the logarithm of zero is $-\infty$ and gives you numerical trouble. So you always want to take the logarithm of a strictly positive number, never of zero. As far as I understand, the choice of $\epsilon=2e-22$ corresponding to a log value of $-50$ is rather arbitrary.