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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.

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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.

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  • $\begingroup$ 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? $\endgroup$ – sandra Feb 7 '20 at 4:55
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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.

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