0
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Do you need any more information for your question? $\endgroup$ – Laurent Duval May 8 at 10:02
0
$\begingroup$

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.

| improve this answer | |
$\endgroup$
  • $\begingroup$ 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 at 4:55
0
$\begingroup$

I tried in an answer to What is the difference between the three types of logarithms? to details why people keep confusing notations (with complement at What is the logarithm of a kilometer? Is it a dimensionless nimber? 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.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.