# log base in log-power spectral features

Is the log in log-power spectral features natural logarithm, or common log of base 10? does it even matter? I found sources for how to calculate it, but they all call it 'log'. no one mentions the base for the logarithm.

The answers provided for this question were insightful though I checked a few papers and finally realized that for log power spectral features (speech separation use cases), natural logarithm is used. though this is a very specific use case and both common base-10 log and natural log can be used in speech processing depending on the application.

It's not particularly important since the different bases just result in a different overall scale factor, but the basic shapes are the same.

This being said, any actual numbers need to be defined with a specific bases otherwise it's ambiguous. The most common is the $$dB$$ which (for power) is defined as $$L = 10 \cdot log_{10}(P/P_0)$$

i.e. it uses base 10.

• what about speech processing? if it is said that log-spectral features are used in speech enhancement or separation, is there a commonly-used base for logarithm in that? – sandra Feb 7 '20 at 4:55

I tried in an answer to What is the difference between the three types of logarithms? to explain why people keep confusing notations (with complement at What is the logarithm of a kilometer? Is it a dimensionless number? or Pa$$^2$$/Hz to dB/Hz conversion).

Logarithms provide you with scale independent measure, summarized as: in base $$b$$, with a positive quantity $$Q$$ affected with power $$p$$:

$$\log_b (Q^p) = \frac{p}{\log b}\log Q$$

So whatever the logarithmic base, whatever the power affected to the quantity $$Q$$ (energy, etc.), they will differ only by a multiplying factor ($$\frac{p}{\log b}$$). If you look at relative quantities, you will get an affine relation:

$$\log_b (Q/Q_0)^p = \frac{p}{\log b}(\log Q-\log Q_0)$$

However in DSP (putting information theory aside), $$\log_{10}$$ is most common.